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Task oriented simulation and control of a wheelchair mounted robotic arm

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Title:
Task oriented simulation and control of a wheelchair mounted robotic arm
Physical Description:
Book
Language:
English
Creator:
Farelo, Fabian
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
Rehabilitation robotics
Dual-trajectory
Mobile robot
Manipulator
Redundancy
ADL
Dissertations, Academic -- Biomedical Engineering -- Masters -- USF   ( lcsh )
Genre:
non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: The main objective of my research is to improve the control structure for the new Wheelchair Mounted Robotic Arm (WMRA) to include new algorithms for optimized task execution; that is, making the WMRA a modular task oriented mobile manipulator. The main criterion to be optimized is the fashion in which the wheelchair approaches a final target as well as the starting and final orientation of the wheelchair. This is a novel approach in non-holonomic wheeled manipulators that will help in autonomously executing complex activities of daily living (ADL) tasks. The WMRA is a 9 degree of freedom system, which provides 3 degrees of kinematic redundancy. A single control structure is used to control the WMRA system, which gives much more flexibility to the system. The combination of mobility and manipulation expands the workspace that a mobile base attains to a manipulator. This approach opens a broad field of applications: from maintenance and storage to rehabilitation robotics. This structure is based on optimization algorithms that can resolve redundancy based on several subtasks: maximizing the manipulability measure, minimizing the joint velocities (hence minimizing the energy), and avoiding joint limits. This work utilizes redundancy to control 2 separate trajectories, a primary trajectory for the end-effector and an optimized secondary trajectory for the wheelchair. Even though this work presents results and implementation in the WMRA system, this approach offers expandability to many wheeled base mobile manipulators in different types of applications. The WMRA usage was simulated in a virtual environment, by developing a test setting for sensors and task performance. The different trajectories and tasks can be shown in a virtual world created not only for illustration purposes, but to provide training to the users once the system is ready for use.
Thesis:
Thesis (M.S.B.E.)--University of South Florida, 2009.
Bibliography:
Includes bibliographical references.
System Details:
Mode of access: World Wide Web.
System Details:
System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Fabian Farelo.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 133 pages.

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University of South Florida
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Resource Identifier:
aleph - 002069513
oclc - 608539316
usfldc doi - E14-SFE0003294
usfldc handle - e14.3294
System ID:
SFS0027610:00001


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ABSTRACT: The main objective of my research is to improve the control structure for the new Wheelchair Mounted Robotic Arm (WMRA) to include new algorithms for optimized task execution; that is, making the WMRA a modular task oriented mobile manipulator. The main criterion to be optimized is the fashion in which the wheelchair approaches a final target as well as the starting and final orientation of the wheelchair. This is a novel approach in non-holonomic wheeled manipulators that will help in autonomously executing complex activities of daily living (ADL) tasks. The WMRA is a 9 degree of freedom system, which provides 3 degrees of kinematic redundancy. A single control structure is used to control the WMRA system, which gives much more flexibility to the system. The combination of mobility and manipulation expands the workspace that a mobile base attains to a manipulator. This approach opens a broad field of applications: from maintenance and storage to rehabilitation robotics. This structure is based on optimization algorithms that can resolve redundancy based on several subtasks: maximizing the manipulability measure, minimizing the joint velocities (hence minimizing the energy), and avoiding joint limits. This work utilizes redundancy to control 2 separate trajectories, a primary trajectory for the end-effector and an optimized secondary trajectory for the wheelchair. Even though this work presents results and implementation in the WMRA system, this approach offers expandability to many wheeled base mobile manipulators in different types of applications. The WMRA usage was simulated in a virtual environment, by developing a test setting for sensors and task performance. The different trajectories and tasks can be shown in a virtual world created not only for illustration purposes, but to provide training to the users once the system is ready for use.
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Task Oriented Simulation And Control Of A Wheelchair Mounted Robotic Arm by Fabian Farelo A thesis submitted in partial f ulfillment of the requirements for the degree of Master of Science in Biomedical Engineering Department of Chemical and Biomedical Engineering College of Engineering University of South Florida Major Professor: Rajiv Dubey, Ph.D. Redwan Alqasemi, Ph.D Kyle Reed, Ph.D. Date of Approval: November 5, 2009 Keywords: rehabilitation robotics, dual trajectory, mobile robot, manipulator, r edundancy, adl Copyright 2009 Fabian Farelo

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Acknowledgments I would like to thank God for giving me the strength, patience and love for what I do. This allowed me to carry out this important part of my lif e. I would like to thank my parents Guzman and Ony for giving me the opportunity to come to the United States to pursue my undergraduate studies. Without their love and sacrifice this would not have be en possible. Thanks to my sister Natalia for making me laugh whenever we talked. I am also very thankful to Dr. Rajiv Dubey for giving me the opportunity to pursue my graduate studies as one of his graduate students. I would like to thank him for his support and encouragement throughout these past 2 years. I would like to thank Dr. Redwan Alqasemi and Dr. Kathryn De Laurentis for their invaluable support and guidance during my Masters program. Im grateful to Dr. Kyle Reed for accepting to be in my thesis committee at such a short notice; thanks for your interest in my work and your eagerness to help. I am very grateful to my lab partners I would like to thank them for their help and companionship inside and outside the university. Thanks to Ana for believing in me. Lastly, I would like to thank my uncles in Miami Rita and Jaime for their unconditional support throughout my stay in this country. Thanks to all of my friends in Tampa and Barranquilla my hometown, for supporting me all the time!

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i Table of Contents List of Tables iii List of Figures iv A bstract vi Chapter 1: Introduction 1 1.1 Motivation 1 1.2 Thesis Objectives 2 1.3 Thesis Outline 3 Chapter 2: Background 5 2.1 Wheelchair Mounted Robotic Arms 5 2.1.1 Commercially Available Prototypes 6 2.1.2 USF WMRA First Prototype 8 2.1.3 Composite Materials in Robotic Arms 9 2.1.4 USF WMRA Prototype Improvements 11 2.2 Redundant Mobile Manipulators 12 2.3 Virtual Reality Environments 14 Chapter 3: Virtual Reality Environment 17 3.1 Virtual Reality Modeling Language 17 3.2 Object Definition 18 3.2.1 Object Visualization 20

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ii Chapter 4: Dual Trajectory Control 26 4.1 Trajectory Generation 27 4.1.1 Activities of Daily Living 27 4.1.2 Trajectory Subtasks 28 4.1.3 Trajectory Stages 28 4.1.4 Trajectory Planning 28 4.2 WMRA Combined Kinematics 31 4.3 Redundancy Resolution and Optimization 34 4.4 Secondary Trajectory Planning 36 4.5 Criteria Functions 39 4.5.1 Joint Limit Avoidance 39 4.5.2 Weighted Optimization 40 Chapter 5: Results and Discussion 43 Chapter 6: Conclusions and Future Work 54 References 56 Appendices 60 Appendix A. Virtual Reality Modeling Language 61 Appendix B. Matlab Functions 89

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iii List of Tables Table 1 Object Definition 20

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iv List of Figures Figure 1 Raptor Arm 7 Figure 2 Manus Arm 7 Figure 3 WMRA I 9 Figure 4 Mechatron ic Joint Design of the DLR LWR III [16] 10 Figure 5 New WMRA Prototype SolidWorks Model 11 Figure 6 4WD Omni Directional Wheelchair [25] 14 Figure 7 Virbot Subsystems Scheme [25] 15 Figure 8 Virtual Reality Environment Snapshot 19 Figure 9 Snapshot of the Couch in VR Environment 21 Figure 10 Environment Snapshot with Boxes in Place 22 Figure 11 Snapshot of the Environment with the Table in Place 23 Figure 12 Snapshot of the Environment with the Sink in Place 24 Figure 13 Snapshot of the Environment with the Shelf and the Book in Place 25 Figure 14 WMRA Coordinate Frames 31 Figure 15 A General Case of the Three Stages for the Secondary Trajectory to be Followed by the Wheelchair 37 Figure 16 Definition of Optimization Variables 38 Figure 17 Gradient Variable Limits for the First Wheelchair Trajectory Stage 40 Figure 18 Circular Path Matlab Animation 44 Figure 19 Joint Angular Displacement vs. Time for Circular Path 45

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v Figure 20 Virtual Reality Simulation Sequence for Approach and Open Door Task 47 Figure 21 3D Endeffector Trajectory for Approaching Task 49 Figure 22 Wheelchair Position Vs. Time for Approaching Task 50 Figure 23 Wheelchair Orientation Vs. Time for Approaching Task 51 Figure 24 VR Sequence of a Second "Ope n Door Task" 52 Figure 25 VR Sequence Book Pick Up 53

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vi Task Oriented Simulation and Control of a Wheelchair Mounted Robotic Arm Fabian Farelo A BSTRACT The main objective of my research is to improve the control structure for the new Wheelchair Mounted Robotic Arm (WMRA) to include new algorithms for optimized task execution; that is making the WMRA a modular task oriented mobile manipulator. The main cr iterion to be optimized is the fashion in which the wheelchair approaches a final target as well as the starting and final orientation of the wheelchair. This is a novel approach in nonholonomic wheeled manipulators that will help in autonomously executin g complex activities of daily living (ADL) tasks. The WMRA is a 9 degree of freedom system, which provides 3 degrees of kinematic redundancy. A single control structure is used to control the WMRA system, which gives much more flexibility to the system. The combination of mobility and manipulation expands the workspace that a mobile base attains to a manipulator. This approach opens a broad field of applications: from maintenance and storage to rehabilitation robotics. This structure is based on optimizatio n algorithms that can resolve redundancy based on several subtasks: maximizing the manipulability measure,

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vii minimizing the joint velocities (hence minimizing the energy) and avoiding joint limits. This work utilizes redundancy to control 2 separate traject ories, a primary trajectory for the endeffector and an optimized secondary trajectory for the wheelchair. Even though this work presents results and implementation in the WMRA system, this approach offers expandability to many wheeled base mobile manipula tors in different types of applications. The WMRA usage was simulated in a virtual environment, by developing a test setting for sensors and task performance. The different trajectories and tasks can be shown in a virtual world created not only for illustr ation purposes, but to provide training to the user s once the system is ready for use

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1 Chapter 1: Introduction 1.1 Motivation According to the latest available data from the US Census Bureau [ 1 A wheelchair mounted robotic arm provides mobility and manipulation capabilities enhancement to these persons. The workspa c e of the system allows the reach of objects that w e re otherwise impossible to reach. On the other hand, it also provides independence from external human aide, since the arm is mounted on the wheelchair and powered by its batteries. There are 2 commercially available WMRAs, the Manus from Exact dynamics in the Netherlands and the Raptor from Applied Resources in the US. Two prototypes of WMRAs have been designed and developed at the University of South Florida, and this work intends to build upon the performance of the system to overcome the limited commercial success that previous attempts have had, such as low payload and ], about 54.4 million Americans had some level of disability, 34.9 million of them had a severe disability. About 11 million Americans older than 6 years of age needed personal assistance with one or more activities of daily living (ADL). This work focuses on people with limited upper a nd lower extremity mobility due to spinal cord injury or dysfunction, or genetic predispositions. Robotic aides used in these applications vary from advanced limb orthosis to robotic arms [ 2].

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2 difficulty to be maneuvered by the final user. T his work intends to transf orm the WMRA system into a task oriented mobile manipulator with the objective of aid ing persons with disability to successfully perform activities of daily living Several methods for optimization can still be used as constrains for redundancy resolution in the WMRA. The absence of th e s e constrains causes an undesired completion of the tasks, and requires a higher input level from the final user. The WMRA control algorithm combines mobility and manipulation for task oriented performance; however, each task is different and requires a different subroutine sequence in terms of trajectory generation for both the endeffector and the wheelchair. 1.2 Thesis Objectives The main objective of my research is to improve the control structure and performance of the WMRA to include complete sequences of tasks that utilize redundancy to optimize the wheelchair and arm motion for autonomous task execution. The main criterion to be optimized is the fashion in which the wheelchair approaches a final target as well as the starting and final orientation of the wheelchair. This is a novel approach in nonholonomic wheeled manipulators that will increase the ease of the task execution for the final user since the system will orient itself depending on the desired task. The WMRA usage will be simulated in a virtual environment by developing a test setting for sensors and task performance. The different trajectories for each task can be shown in a virtual world created not only for illustration purposes, but to provide traini ng

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3 to the user once the system is ready to be used. The objectives are summarized as follows: Develop new criterion functions for the optimization of the translation and orientation of the wheelchair and the end effector in a specific task Develop a refine d test bed for the WMRA system for experimentation in task performance, and trajectory generation. Develop program modules for several ADl tasks creating subroutines for each task to autonomously execute. Create a virtual reality environment to test the algorithm and to train the user on the WMRA use while collecting data for further development and improvements 1.3 Thesis Outline This thesis will provide a literature review and present the state of the art on the important subjects regarding this work in chapter 2. Chapter 3 presents the trajectory generation problems. The reader is given an overview of the proce dures implemented in this work. Chapter 4 presents the Virtual Reality environment developed for the simulation of the system. Chapter 5 presents the detailed procedure followed to achieve a dual trajectory control in the WMRA for performing activities of daily living. Chapter 6 presents the results in Virtual Reality simulation and Matlab graphics following the main variables of the system. A d iscussion of these results is also addressed in this chapter. The final chapter briefly goes over the conclusions of this thesis and proposes future

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4 work that can be completed later A list of references and appendi c es are presented at the end with the code implemented in this thesis.

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5 Chapter 2: Background In this chapter, the state of the art in the research area is presented to the reader. This includes research in rehabilitation robotics, mobile manipulators, redundant robots, virtual reality environments and previous work developed in wheelchair mounted robotic arms. 2.1 Wheelchair Mounted Robotic Arms Several designs of workstationbased robotic arm systems were developed over the years, such as Handy 1 [ 3], RAIL project [ 4], ProVAR [ 5] and the design conducted by Gunnar Bolmsjo, et al. [ 6]. WMRA combines the idea of a workstation and a mobile base robot to mount a manipulator arm onto a power wheelchair. The most important design consideration of where to mount a robotic arm in a power wheel chair is the safety of the operator [ 7 ]. WMRA can be mounted in the front, side or rear of the wheelchair [ 8].

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6 2.1.1 Commercially Available Prototypes The two commercially available commercial WMRAs utilize side mounting on a power wheelchair. These t wo commercial arms are the Manus, manufactured by Exact Dynamics; and the Raptor, manufactured by Applied Resources. The Manus manipulator arm can be programmed in a manner comparable to industrial robotic manipulators. It has been under development sinc e the mid 1980s and it entered into production in the early 1990s [ 9]. It is a 6 DOF arm, with servomotors all housed in a cylindrical base as shown in figure 1. Another production WMRA is the Raptor [ 10], which mounts to the right side of the wheelchair. T his manipulator has four degrees of freedom plus a planar gripper as shown in figure 1. The user directly controls the arm joints with either a joystick or a 10 button controller. Typically, the joystick that controls the manipulator arm is located on the armrest opposite to the input device that controls the steering of the power wheelchair. Because the Raptor does not have encoders, the manipulator cannot be controlled in Cartesian coordinates. This compromise was done to minimize the overall system cost.

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7 Figure 1 Raptor Arm Figure 2 Manus Arm

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8 2.1.2 USF WMRA First Prototype Previous work has shown the analysis of commercial WMRAs and the development of a wheelchair mounted robotic arm (WMRA I) system with combined mobility and manipulation control [ 11,12, 13 The arm carries seven revolute joints and a gripper designed for ADLs. The gripper [ 14] is powered by a Faulhaber coreless DC servomotor that is compact and capable of producing 6N of grasping force at the gripper paddles. In order for t he WMRA to have more commercial success, the weight must be reduced and the payload needs to be increased. Reducing the overall weight of the robot arm that is attached to the power wheelchair will reduce the power consumption, allowing longer system usage before the batteries need to be recharged. A lighter weight WMRA will also be less restrictive on the allowable user weight because the WMRA is an aftermarket modification and power wheelchairs are rated for a maximum weight capacity by the manufacturer ]. The WMRA I is comprised of a seven degree of freedom robot arm, a gripper, and a power wheelchair as shown in figure 3. That system was designed to use Matlab to control the arm and the chair motion with a single graphical user interface (GUI) which can be used to control the end effector in Cartesian space. User interfaces include a touch screen, a spaceball with 3 D input capabilities and a Brain Computer Interface (BCI) that uses the stimulated P 300 signal.

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9 Figure 3 WMRAI 2.1.3 Composite Materials in Robotic Arms Industrial robotic arm companies have begun to use composite materials, such as carbon fiber, as major structural components to reduce weight while keeping the necessa ry structural strength [ 15 The DLR research gro up has been working on producing the lightweight robot (LWR) arm for industrial usage [16] specifically for packaging robots, but it also has attributes that allow it to be used for human interaction. They have developed two LWR ], but they have not been widely used in the field of rehabilitation robotics, specifically for WMRAs. Utilizing these composites in the construction of a WMRA can help reduce the weight of the overall design.

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10 arms previous to the current arm, both of which have been improved upon in multiple areas [ 16]. The LWR I is a seven degreeof freedom robot arm that used carbon fiber for its structure. It also utilized double planetary gear heads and torque sensing for control, both of whic h proved to be issues for manufacturing or robustness. DLR then developed the LWR II which used harmonic drive gear heads instead of the double planetary gears as well as incorporating a feedback system for joint torque and motor and link position. All o f the electronic systems were housed inside the arm, eliminating the external control box, which most industrial robots have. Figure 4 Mechatronic Joint Design of the DLR LWR III [ 1 6 ]

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11 2.1.4 USF WMRA Prototype Improvements Based on this advances in the state of the art, a n attempt was made to us e a different material for a lighter arm using pultruded carbon fiber tubes as the structural member of each of the three main links of the arm [ 17 ] However, due to the material failu re a new design is already under development Figure 5 New WMRA Prototype SolidWorks Model This design returns to the aluminum tubes used in the WMRA I. However, the thickness of the tubes was reduced and the links and brackets are bolted instead of welded for better maintenance and aesthetics. The motors used for the second prototype

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12 are also smaller in size, while keeping the same torque capabilities, accounting for a big percentage of weight reduction. 2.2 Redundant Mobile Manipulators Redundant mobile manipulators as a research topic have gained interest with its potential for a wide range of applications. In [ 18], a 7 DoF mobile manipulator consisting of a 5 DoF arm mounted on a 2 DoF wheeled platform was controlled by coordinating the platform motion and the gripper motion. The platform was driven to a destination that put the target within the grippers workspace. The nonholonomic wheeled platform of manipulators was addressed in [ 19 Path planning for nonholonomic mobile robots has been addressed by researchers for more than 2 decades. In [ 20], this was implemented for obstacle avoidance and implemented using the nonholonomic constrains of the platform. However, combining this c onstrains with a redundant manipulator was not considered at that time. In [ ], where redundancy for a planar mobile manipulator was resolved using extended reduced gradient and projected gradient optimization based methods. This approac h was tested in simulation by having the end effector pointing at a pre specified orientation while the wheelchair followed a circular trajectory, however they did not attempt to control two separate trajectories for the end effector and the non holonomic base. 21], an online planner for obstacle avoidance with moving targets was presented. Their model is

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13 suitable for real time generation of trajectories and it was tested in crowded simul ated environments. Recent work in redundancy resolution of mobile robots has accomplished the task of sustaining separate trajectories for the end effector and the platform. In [ 22] they implemented redundancy resolution of a 2D mobile manipulator using independent controllers developed within each others decoupled space, which facilitated the redundancy resolution at a dynamic level. The separate trajectories will be controlled by extending the weighted least norm solution method [ 23 Some applications with mobile platforms have implemented four wheel drives to account for a better accuracy of the platform motion. In [ ] to constrain or priori tize the motion of the platform to follow certain trajectories. This method was intended for resolving redundancy while minimizing unnecessary motion of the joints. This approach has also been used along with specific criterion functions to avoid joint lim its [24]. 25] a patented omnidirectional mobile platform with 4 wheel drive was used for wheelchair applications.

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14 Figure 6 4WD Omni D irectional Wheelchair [25] In the paper the kinematics of the 4WD platform are analyzed and they developed a control method for omnidirectional motion. This includes the addition of a third motor for the rotation of the chair. This an application that can improve the nonholonomic constrains that are attached to WMRAs. 2.3 Virtual Reality Environments Testing and simulation is an important step in every design process. In WMRAs the main design factor is the safety of the operator [ 7]. For this, 3D animations and simulations turn into a useful tool to test the behavior and robustness of the algorithms before coding it into the physical system. Previous wor k has shown the good use of

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15 virtual environments for simple mobile robots [26, 27 In [ 25, 26] the authors describe a robotics architecture developed for their particular system called VIRbot. It is a robot designed for action planning using AI concepts. A virtual environment is implemented by the description of the working environment of the robot. ] to prove the control concept in simulation. Figure 7 Virbot S ubsystems S cheme [ 25 ] The virtual environment is shown in 3D using a system called ROC2. This system uses C /C++ as its main platform, whic h also reads from the sensors and the main robot

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16 program. This system uses the virtual environment as a tool to compare the actual environment with the one generated by the sensors. This is a very promising application but it does not provide the ability of running the simulation offline to test the control program as it is intended in this work.

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17 Chapter 3: Virtual Reality Environment Testing and simulation is an important step in every design process. In WMRAs the main design factor is the safety of the operator [ 7]. For this, 3D animations and simulations turn into a useful tool to test the behavior and robustness of the algorithms before coding it into the physical system. Previous work has shown the good use of virtual environments for simple mobile robots [ 25, 26] to pro ve the control concept in simulation. This wor k uses the virtual environment as a tool to modify and debug the control system and check for the users safety before implementing it on the physical arm. 3.1 Virtual Reality Modeling Language The Virtual Reality Modeling Language (VRML) is the language used to display three dimensional objects in a browser. It is considered a 3 D web standard. Since 1994 VRML1 has been implemented in several browsers, but it allowed only the creation of static virtual worlds. This limitation reduced its widespread use. The VRML2 or VRMl97 standard was created to overcome this issue and add animation and interactivity to a

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18 virtual world. VRML97 represents an open and flexible platform for creating interactive thr ee dimensional scenes (virtual worlds) [ 28]. Using Matalb Virtual Reality Toolbox a communication between the control program and the virtual worlds can be established. This adds to the main program the versatility of a 3 D animation to monitor the simulated WMRA performance. 3.2 Object Definition The virtual environment designed for the WMRA is made of several dynamic and static objects. The objects included in this simulation were created in three different ways. For simple objects such as boxes or walls the VRML code was typed to create the geometry, texture, location, scale and m aterial properties. For moderately complicated geometries such as a table or a couch the VR builder tool was used. This application allows the creation of simple primitives as a CAD program and then converts the part into VRML code. For highly complicated components such as the wheelchair and the robotic arm SolidWorks was used. Once the part is completed it can be easily exported into VRML files, keeping the same reference frame used in the CAD drawing. Some of the objects are included in the control loop, while others only move when there is a collision or the WMRA performs a specific task Figure 8 shows a snapshot of the VR environment created for ADL applications.

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19 Figure 8 Virtual Reality Environment Snapshot Table 1 shows a summarized description of the main elements developed for the virtual reality environment. The type of element shows if the element moves within the environment. The creation field specifies which type of procedure was used for its generation. And the control field presents the role of the object in the control of the simulation

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20 Table 1 Object Definition 3.2.1 Object Visualization In this section, snapshots of the main components of the VR environment are presented. These components, and the procedure used for their creation are listed in table 1. The first object to be presented is the couch. This object was made using VRBuilder. This software is part of Matlab Virtual Reality Toolbox and has simple geometry primitives as well as a commando prompt for VRML code input. The couch used for the simulation consists of a combination of cylinders cubes and spheres in most of t he edges. VRBuilder also allows the implementation of textures. Figure 9 shows a snapshot of the couch presented in the virtual reality simulation. Object Type Creation Control WMRA DynamicSoldWorks Control Loop Walls Static TypedN/A Floor Static TypedN/A Laser Dynamic VRBuilder Control Loop CouchStatic VRBuilder N/A Table Static VRBuilder N/A Shelves Static VRBuilder N/A Switches Dynamic VRBuilderCollision Doors Dynamic VRBuilderCollision Boxes DynamicTyped Collision Sink SoldWorksN/A

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21 Figure 9 Snapshot of the Couch in VR Environment The simplest objects in the simulation are the boxes. These were typed manually since it consists only of a box geometry primitive. Figure 10 shows a snapshot of the environment with the boxes in place. These objects will be used in future work for obstacl e avoidance control.

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22 Figure 10 Environment Snapshot with Boxes in Place A table was made to simulate pick and place tasks and also for obstacle avoidance. The table was also created with VRBuilder and it consisted of cylinder primitives mostly. Figure 1 1 shows an auxiliary view of the table in the environment.

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23 Figure 11 Snapshot of the Environment with the Table in Place A sink w as simulated to include several ADLs for future work. For instance it has doors to simulate an opening door task, but it also has a tab and a higher small shelf for object placement. Figure 12 shows a snapshot of the sink that is used in the simulation.

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24 Figure 12 Snapshot of the Environment with the Sin k in Place A shelf and a book were also developed for the environment. The shelf and the book were both made using Solid Works. The parts can be saved as wrl files directly from the CAD program. The main objective for these objects is to simulate a pick and place task.

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25 Figure 13 Snapshot of the Environment with the Shelf and the Book in Place The objects developed for the simulation can be interfaced through Matlab and the Virtual Reality Toolbox. The configuration of the environment can be easily modified by entering the transformation matrix of the objects.

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26 Chapter 4: Dual Trajectory Control This is the core chapter of this thesis. The combination of the wheelchair mobility and the arm manipulation in an optimized redundancy resolution algorithm [ 24 ] allowed for the possibility of programming pre set ADL tasks to be autonomously executed. Some ADL tasks require wheelchai r orientation control to place the WMRA in a configuration that makes the task possible. In this context, having a secondary trajectory for the wheelchair to follow while the arm is following its main trajectory allows for an easier task execution. This wo rk utilizes redundancy to control 2 separate trajectories, a primary trajectory for the end effector and an optimized secondary trajectory for the wheelchair. Even though this work presents results and implementation in the WMRA virtual reality simulation environment, this approach offers expandability to many wheeled base mobile manipulators in different types of applications. In this work, we develop and optimize a control system that combines the manipulation of the robotic arm and the mobility of the wh eelchair in a single control algorithm. Redundancy resolution is to be optimally solved to avoid singularities and joint limits. While the end effector follows a primary trajectory, we introduce a secondary trajectory to be followed by the wheelchair as pa rt of the redundancy resolution and optimization algorithm.

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27 4.1 Trajectory Generation 4.1.1 Activities of Daily Living The main objective of the WMRA system is to maximize the manipulation capabilities of persons with disabilities who are confined to a wheelchair. This objective is reached by enhancing the performance of certain tasks that are regularly carried out every day. Activities such as turning a light switch, grabbing a cup or a book, picking up objects from the floor, opening a drawer, a cabinet or a door, are referred to as activities of daily living (ADL). As expressed in the introduction of this chapter, the main control objective of the system is to carry out a desired end effector trajectory. That is how activities of daily living gain importance in the control of the system; each ADL is comprised of one or several different trajectories that will need to be programmed and executed by the WMRA to complete a full task. A set of ADLs can be prespecified towards turning the WMRA into a task or iented mobile manipulator in which the cognitive load of the user will be significantly reduced; that is by reducing the need to specify the different trajectories needed to carry out a certain task. For instance, a subset of linear and circular trajectories that are needed to open a door can be specified to be performed autonomously by the system; therefore, all that is left to be specified are the door variables (knob location, width, side to open). A simulation of the WMRA carrying out this ADL is presen ted in the chapter 5.

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28 4.1.2 Trajectory Subtasks As described in the previous subsection, every ADL can be divided into a set of trajectories that need to be executed by the system to complete a certain task. This subsection intends to provide a sense of how the trajectories are subdivided to be completed as a whole task by the WMRA 4.1.3 Trajectory Stages End effector trajectory and wheelchair trajectory are used as a primary and secondary trajectory respectively throughout this work. A trajectory stage is a term we use to pinpoint a certain portion of the trajectory to be followed in a certain period of time. Also there might be a stage in which no motion is required by the wheeled base while the e ndeffector is carrying out a specific trajectory. A trajectory stage is then defined as a portion of the task that follows a specific combination of motions by the WMRA to partially fulfill a desired task that is composed by several trajectories. 4.1.4 Tr ajectory Planning For any given task to be programmed in a manipulator, a path needs to be followed. The orientation part of the trajectory can be represented in a single rotational angle that makes it possible to divide the path into angle steps along th e trajectory. The single angle of rotation can be found from the homogeneous transform as [ 29 ) a o (n ) o (n ) n (a ) a (oz y x x y z x y z1 tan 2 2 2 1 ]: (1)

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29 where a typical homogeneous transformation matrix consists of three rotational vectors and one translational vector: 0001xxxx yyyy zzzznoaP noaP T noaP Once we have the single angle of rotation and the axis of rotation, we can generate the trajectory using a linear equation. The approach used to generate the trajectory utilizes a constant transformation change along the trajectory, which means that between every two consecutive points in the trajectory. This trajectory generation solves the problem of going from one point to another, however, going f rom rest to a full joint speed in no time and vice versa generates a discontinuous acceleration at the beginning and at the end of the trajectory, and therefore a linear trajectory is not the most adequate when the start and finish velocity is zero To tak e care of the problems of linear trajectory, a polynomial trajectory is introduced so that when the arm starts from rest, the trajectory points are very close to each other, and then the arm will reach a maximum speed and ramp back down to zero velocity wh en it reaches the destination. The governing equation for such a polynomial can be written for any variable that needs to be ramped as follows: 3 0 3 2 0 2 02 3 t ) X X ( t t ) X X ( t X ) t ( Xf f f f (2)

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30 When using the polynomial function to generate a nonlinear trajectory, efficiency of the trajectory following task was not acceptable. The reason is that the desired velocity is reached at the mid point of the trajectory, and ramping that velocity up and down takes a very long time. To overcome this problem, a polynomial blending procedure was adopted [ 30]. The blending factor accelerates the velocities at the beginning of the trajectory, and then set the acceleration to zero throughout the major part of the trajectory when the desired velocity is reached, and then decelerate the velocity back down to zero at the end of the trajectoryfollowing task. We first begin by defining the blending factor b, a constant from 0 to 10. Then we define the acceleration during blending as: 24f i f bt X X b X (3) Where tf X ) X X ( X t X t ti f f b 2 4 22 2 is the time at which the trajectory following task is completed. Then we define the time when blending ends as: (4) For each ADL to be performed by the WMRA a set of trajectories have to be generated. Details on the optimization algorithm for th e combined mobility and manipulation of the system can be found in previous publications [12, 24].

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31 This procedure can be implemented with any type of trajectory. Any trajectory will be divided in steps according to the specified method. If a circular path is needed then the equation of a circle is programmed and so on. 4.2 WMRA Combined Kinematics Two of the DoFs are provided by the nonholonomic motion of the wheelchair. This subsystem is controlled using 2 input variables: the linear position of the wheelchair along its x axis, and the angular orientation of the wheelchair about its z axis (see fi gure 14). The planar motion of the wheelchair includes three variables: the x and y positions, and the z orientation of the wheelchair [ 31 ]. Figure 14 WMRA Coordinate Frames

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32 Assuming that the manipulator is mounted on the wheelchair with L2 and L3 offset distances from the center of the differential drive across the x and y coordinates respectively (see F igure 14), the mapping of the wheels velocities to the manipulators end effector velocities along its coordinates is defined by: c W c cV J J r (5) where the end effector velocity and manipulator velocity are T cz y x r r l cV and 3 6 2 2 1 3 2 2 2 21 ] 0 [ ] 0 [ ] 0 [ ) (x x x x yg xg yg xg x cS P C P C P S P I J 2 3 1 1 3 2 1 3 2 1 3 2 1 3 2 1 52 2 ) ( 2 ) ( 2 ) ( 2 ) ( 2 2x c c c c c c c c c c c c Wl l s l c l l s s l c l l s c l s l l c c l s l l c l J where Pxg and Pyg are the x y coordinates of the endeffector based on the arm base frame, is the angle of the arm base frame, which is the same as the angle of the wheelchair based on the ground frame and L5 is the wheels radius. The above Jacobian can be used to control the wheelchair and the arm after combining their respective jacobians t ogether. The wheelchair will move forward when both wheels have the same speed and direction while rotational motion will be created when both wheels rotate at the same velocity but in opposite directions. Since the wheelchairs position and orientation ar e our control variables rather than the left and right wheels velocities, Vc can be redefined as:

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33 X Vc (6) where: r rl X and l l 5 1 5, 2 In the previous expression, can be expressed in terms of both r or l since for pure rotation these speeds are equal but in opposite directions. Seven degrees of freedom are provided by the robotic arm mounted on the wheelchair. From the DH parameters of the robotic arm specified in earlier publications [13], the 6x7 Jacobian that relates the joint rates to the Cartesian speeds of the end effector based on the base frame is generated according to Craigs notation [ 28]: A A AV J r (7) where: T Az y x r is the task vector, and T AV7 6 5 4 3 2 1 is the joint rate vector, and JA is the robotic arms Jacobian. Combining the wheelchair and arm kinematics yields the total system kinematics. In the case of combined control, let the task vector be: ) (A cq q f r (8) where qc and qA are the control variables of the wheelchair and arm respectively. Differentiating ( 8) with respect to time gives :

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34 A A c cV q f V q f r A A c W cV J V J J c A W c AV V J J J (9) or V J r (10) where: Tz y x r W c AJ J J J and T T c AX V V V 7 6 5 4 3 2 1 4.3 Redundancy Resolution and Optimization Redundancy is resolved in the algorithm using S R inverse of the Jacobian [ 32] to give a better approximation around singularities, and use the optimization for different subtasks. Manipulability measure [ 33 ) det(TJ J w ] is used as a factor to measure how far is the current configuration from singularity. This measure is defined as (11) The SR Inverse of the Jacobian in this case is defined as: 1 6 *) * ( I k J J J JT T (12) where I6 is a 6x6 identity matrix, and k is a scale factor. It has been known that this method reduces the joint velocities near singularities, but compromises the accuracy of the solution by increasing the joint velocities error. Choosing the scale factor k is cr itical to minimize the error. Since the point in using this factor is to give approximate solution

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35 near and at singularities, an adaptive scale factor is updated at every time step to put the proper factor as needed: 0 0 2 0 00 ) 1 ( w w for w w for w w k k (13) where w0 is the manipulability measure at the start of the boundary chosen when singularity is approached, and k0Weighted Least Norm solution proposed by [ 23] can be integrated to the control algorithm to optimize for secondary tasks. In order to put a motion preference of one joint rather than the other (such as the wheelchair wheels and the arm joints), a weighted norm of the joint velocity vector can be defined as: is the scale factor at singularity. WV V VT W (14) where W is a 9X9 symmetric and positive definite weighting matrix, and for simplicity, it can be a diagonal matrix that represent the motion preference of each joint of the system. For the purpose of analysis, the following transformations are introduced: 2 / 1 W J JW and V W VW 2 / 1 (15) Combining these equations, it can be shown that the weighted least norm solution integrated to the S R inverse is: r I k J W J J W VT T W1 6 1 1* (16)

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36 The above method has been used in simulation of the 9DoF WMRA system with the nine control variables (V) that represent the seven joint velocities of the arm and the linear and angular wheelchairs velocities. An optimization of criteria functions can be accomplished when used in the weighting matrix W. 4.4 Secondary Traje ctory Planning For the completion of an activity of daily living, the main task will be given as a set of trajectories for the end effector to follow. Although the main task is followed, wheelchair position and orientation can be important for the task to be successfully completed. A secondary subtask representing the best position and orientation of the wheelchair is represented as a secondary set of trajectories for the wheelchair to follow. An optimal position/orientation combination of the nonholonom ic motion of the wheelchair can be achieved if the secondary trajectory is divided into 3 stages. The first one is to orient the wheelchair facing its desired linear trajectory. The second stage is to proceed with a linear motion along the secondary trajec tory to approach the final planar coordinates. Once the wheelchair reaches its final position, the third stage will be to orient the wheelchair to its final desired orientation. Figure 15 shows the three stages implemented for the secondary trajectory.

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37 Figure 15 A General C ase of the Three Stages for the Secondary Trajectory to be Followed by the Wheelchair The three stages to be applied for the secondary trajectory will only involve the position X and orientation variables of the wheelchair. The nned for the three stages comes from the non holonomic constrains attached to the wheelchair. There are three variables to be controlled, which are the x and y position as well as the orientation of the wheelchair around the z axis, however there are only two control variables, which are the left and right wheel velocities. For an expanded derivation of these constrains in the WMR A the reader is advised to go through previous work [24] As shown in F igure 16 knowing the initial and final transformations of the ) ( ) ( 2 tani f i fx x y y a (17)

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38 That defines the amount of motion needed for the three stages to be followed in the following order: Rotation by the amount of i 1 Translation by the amount of 2 2) ( ) (i f i fy y x x tr Rotation by the amount of f 2 The above three wheelchair motion values can be utilized in the weight matrix as criteria to enforce the wheelchair motion. Figure 16 Definition of Optimization Variables G y x (,,)iiixyz i 2 f (,,)fffxyz 1 tr

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39 4.5 Criteria Functions The criteria functions used in the weight matrix for optimization can be defined based on different requirements. 4.5.1 Joint Limit Avoidance For the robotic arm, the physical joint limits can be avoided by minimizing an objective function that represents this criterion. One of these mathematical representations was p roposed by [ 23] as follows: 2 7 ,max,min 1 ,max, ,min() 1 () 4( )()ii i iicurrenticurrentiqq Hq qqqq (18) where qi 2 ,max,min ,max,min 22 ,max, ,min()(2 ) () 4( )( )ii icurrentii i iicurrenticurrentiqqqqq Hq qqqqq is the angle of joint i. This criterion function becomes 1 when the current joint angle is in the middle of its range, and it becomes infinity when the joint reaches either of its limits. The gradient projection of the criterion function can be defined as: (19) When any particular joint is in the middle of the joint range, (19) becomes zero for that joint, and when it is at its limit, (1 9) becomes in finity, which means that the joint will carry an infinite weight that makes it impossible to move any further.

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40 4.5.2 Weighted Optimization For the wheelchair, the criteria functions can be defined for each stage of its trajectory based on the desired motion of the wheelchair. Similar to the arm, mathematical representations can be obtained by treating the range of the desired wheelchair motion as a motion limit. The upper limit in this case is set to be the current initial orientation (or position for the second trajectory stage) of the wheelchair. The 1 2Figure 17 (or double the translation distance tr for the second trajectory stage). In this case, the middle of that range will be the desired orientation/ position of the wheelchair, and either limit will be avoided. shows an example of the limits for the first wheelchair trajectory stage. Figure 17 Gradient Variable Limits for the First Wheelchair Trajectory S tage G iii mini maxx

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41 To generalize the representation of the objective function, let variable P be a ) ( ) ( ) ( 4 1 ) (min max 2 min maxP P P P P P P Lcurrent current (20) and the gradient of the criterion function can be defined as: 2 min 2 max min max 2 min max) ( ) ( 4 ) 2 ( ) ( ) ( P P P P P P P P P P P Lcurrent current current (21) For the first stage, when the wheelchairs angle is in the middle of its allowable range, ( 21) becomes zero, and when it is at its limit, ( 21 ) becomes infinity, which means that the variable will carry an infinite weight that makes it impossible to move any further. This value of the gradient will be placed at the translationa l part of the weight matrix. The rotational part on the other hand will start with a very low value for (21) This way, rotational motion in the first stage will be active (with small weight), and the translational motion will be inactive (with high weight). The diagonal weight matrix W can then be constructed as: 1 1 2 2() 00 () 000 0 () 0 () 000XHq w q Hq w q W LX w X L w (22)

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42 where for stages 1 and 3: 2 maxmin maxmin min max 22 max min 2 maxmin maxmin 22 max min()(2 ) () 4()() ()(2 ) () 4()()current currentcurrent current currentcurrentL XXXXX LX Xtol XXXXX At the start of these stages () LX X = () L =0 And for stage 2: 2 maxmin maxmin 22 max min 2 maxmin maxmin min max 22 max min()(2 ) () 4()() ()(2 ) () 4()()current currentcurrent current currentcurrentL tol XXXXX LX XXX XXXXX At the start of stage 2 () LX X = 0 and () L = wiThis procedure can achieve the desired trajectory combinations to successfully execute tasks that require separate end effector and wheelchair trajectories. Examples of ADL tasks were tested in simulation and the results will be presented in the following chapter. is a user set preference value for each joint and the position/orientation of the wheelchair These values can achieve the user preference if joint limits are not approached and wheelchair motion is at its desired position.

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43 Chapter 5: Results and Discussion This chapter presents the results in simulation that have being obtained for this thesis work. The computational work was done in a Core 2 Quad PC with Windows XP OS. Matlab and its virtual Reality Toolbox were used to program and r un the simulation. Trajectory planning is essential for the task programming. Once the WMRA reaches the desired position, autonomous control will be used to follow different trajectories a task may need. The Matlab Graphics simulation allowed keeping track of the variables of concern for the control of the manipulator. The linear trajectory motion has already be en tested for optimal control. More detailed results can be found in previous publications [ 24 ]. WMRA variables were monitored for different end ef fector motion patterns to ensure the smooth completion of ADL tasks that include various trajectory combinations. Most of the trajectories involved in ADLs can be decomposed in several linear and circular trajectories. The next couple of figures present th e result of circular trajectories. Figure 18 shows a snapshot of the Matlab graphics simulation with the WMRA model performing a circular trajectory and Figure 19 shows the joint angular displacement versus time for the completion of a circular trajectory of 1m of radius which is the radius of a typical door.

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44 Figure 18 Circular Path Matlab Animation

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45 Figure 19 Joint Angular Displacement vs. Time for Circular Path To illustrate the simulation, a virtual reality WMRA environment was developed for several activities of daily living. In this section, a Go To and Open the Door task was selected to pro ve the concept. For illustration purposes the initial and final tra nsformations of the endeffector trajectory are known. The initial and final transformations of the wheelchair approach trajectory are also given. The task process is divided into two subtasks. The first task is to approach the door knob while both the e ndeffector and the wheelchair are following their respective trajectories. In this sub task, the end effector follows its straight line trajectory from start

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46 to end, and the wheelchair follows the three stages of its trajectory to approach the door approximately at the desired position and orientation. The second subtask is to open the door inwards while the wheelchair is backing up away from the door. In this subtask, the endeffector follows its circular trajectory to open the door, and the wheelchair follows a single stage straight line trajectory to back up away from the door. The wheelchair orientation during this sub task is kept constant.

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47 Figure 20 Virtual Reality Simulation Sequence for Approach and Open Door Task Initial Position Wheelchair Rotation Forward Motion Forward Motion Wheelchair Rotation Opening Door Opening Door Final Position ---Wheelchair path ---Gripper path ---Wheelchair path ---Gripper path ---Wheelchair path ---Gripper path ---Wheelchair path ---Gripper path ---Wheelchair path ---Gripper path ---Wheelchair path ---Gripper path ---Wheelchair path ---Gripper path ---Wheelchair path ---Gripper path

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48 Figure 20 shows the complete task execution; reaching the door and following a circular path to open it. In that sequence, the transition between figures 20I and 20II shows how the end effector was following its 3D trajectory while the wheelchair was rotating with out translation to reach its trajectory orientation. After reaching an approximate angle equivalent to that of the trajectory line, the wheelchair started moving forward without rotation, while the end effector was still following its trajectory as shown i n figures 20III and 20IV. The transition between figures 20IV and 20V shows how the end effector kept following its 3D trajectory while the wheelchair was rotating back without translation to the desired orientation. Figure 20VI shows the endeffector following the circular trajectory to open the door, and the wheelchair was moving backwards to clear the space for the door to open. Figures 20VII and 20VIII show the completed task of opening the door and arriving at the final pose. Notice here that a third subtask can be added to have the WMRA go through the door. In that case, the endeffector will need to stay stationary while the wheelchair moves forward to go through the door. The first sub task included a 3D trajectory for the end effector as sho wn in Figure 2121, and a planar trajectory for the wheelchair. The second subtask included two planar trajectories since the end effector is opening t he door in a planar motion.

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49 Figure 21 3D End effector Trajectory for Approaching Task Note that the secondary trajectory will not be followed in a precise motion. As the weights of the wheelchair position and orientation are updated at every iteration in the weight matrix, the relative motion is kept to minimum for the undesired variable mo tion, while the relative motion of the desired variable is kept to maximum. Figure 22 and 23 show the resulting wheelchair motion in its three position /orientation stages for the first subtask of approaching the door. In Figure 22, it can be seen that the position stayed close to its desired traject ory throughout the wheelchair motion. Orientation, however, seems to have slightly higher error in following its desired orientation as seen in Figure 23.

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50 Figure 22 Wheelchair Position Vs. Time for Approaching Task In some extreme cases, fail ure can occur when this algorithm is used due to the fact that it is impossible to achieve both trajectories at the same time. An example of that is when the endeffector is commanded to go in a direction that is deviating away from the desired wheelchair dir ection. It is shown, however, that even if the subtask that is being performed by the wheelchair fails at certain instances, the trajectory following of the endeffector stays unaffected. There is a slight offset from the desired path and the actual path covered by the wheelchair. This is an optimizazion process and the results are always going to be approximates. The reason for this error is because the end effector is trying to follow its commanded trajectory and the arm is stretching to its limit while the wheelchair is still

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51 rotating. At this point, the wheelchair trajectory is compromised and the wheelchair starts to move forward so that the end effector keeps up with its trajectory following task. It was also noted that the wheelchair accelerates forw ard in its "stage 2" motion faster than the gripper so that it accounts for the time it will take to perform "stage 3" rotation while the endeffector is still moving along its final steps of its trajectory. Figure 23 Wheelchair Orientation Vs. Time for Approaching Task The same issue is presented for the wheelchair orientation while approaching the target. Even if the ideal path is set to rotate quickly and start moving forward, even when the wheelchair starts movin g the desired rotation angle is not reached. Therefore, the wheelchair will keep rotating as long as the end effector trajectory remains unaltered. This issue could also be present in the stage three. If the time for the wheelchair rotation is not accurately coordinated, the final orientation may be achieved once the endeffector has already reached its final destination This example assumes that the door opens towards the wheelchair and towards the left side of the user. If the door opens to the right side of the user while the robotic arm is

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52 mounted on the left side of the user, a more complicated trajectory is required to achieve acceptable results. Programming several sequences of trajectories for both the wheelchair and the endeffector can be utilized to form a complete set of tasks that can be autonomously preformed to make the WMRA system a taskoriented system. A second orientation of the door is presented in an aerial view to illustrate the efficiency of the algorithm (see Figure 24) Figure 24 VR Sequence of a Second "Open Door Task" Figures 24I and 24II show a sequence of the WMRA approaching the door knob, and 24III and 24IV show the opening of the door. This task is the most complex tasks since it includes th e dual trajectory track to approach an object as well as different types of trajectories, for instance it includes a circular trajectory to be followed to open the door. Having successfully performed this I IV III II

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53 task allows the implementation of several trajectories in series to perform any other simpler ADL task. Figure 2 5 shows the sequence to approach and pick up a book. Figure 25 VR Sequence Book Pick Up In Figures 2 5I and 25II, the WMRA is approaching the shelf where the book is. Once the book is reached in 25III, the transformation of the book will be the same of that of the gripper. In a humanlike motion the book is pulled back and the user can either take it or command the WMRA to place it somewhe re else. I IV III II

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54 Chapter 6: Conclusions and Future Work Optimized dual trajectory following control system was presented for a 9 DoF redundant wheelchair mounted robotic arm system to be used for people with disabilities to help them in their ADL tasks. S R i nverse was used with a weighting matrix to solve for the resolved rate solution to follow a primary trajectory. A secondary trajectory for the wheelchair to follow was mathematically represented and implemented for a Go To and Open the Door task. Joint l imits for the manipulator joint variables and the position/orientation variables for the wheelchair were used in the weight matrix to prioritize or penalize the motion of the nine control variables. A simulation of the task in virtual reality simulation an d the results were presented. Future work includes the addition of a pool of ADL tasks in the program and the incorporation of a laser range finder to obtain position information of the target and the environment. Implementation of the control system will be done in the new prototype WMRA under development. Clinical human testing of actual ADL tasks will follow, and data will be collected and presented in future publications An Ongoing effort in the implementation of a Brain Computer Interface (BCI) as a user interface is also part of the future work to be accomplished for this work. This will allow the control of the system by persons with more severe disabilities such as loc ked in

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55 syndrome. The implementation of different programming languages for the control of t he system is also being tested.

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56 References [ 1] US Census Bureau, Americans with disabilities , Census Brief December 2008, http://www.census.gov/prod/2008pubs /p70117.pdf [ 2] Reswick J.B., The moon over dubrovnik a tale of worldwide impact on persons with disabilities, Advances in External Control of Human Extremities 1990. [ 3] Topping, M.J., The development of handy1, a robotic system to assist the severely disabled, Proc ICORR 99, pp. 244249, 1999. [ 4] Topping, M., Heck, H., Bolmsjo, G., and Weightman, D., 1998, The development of RAIL (Robotic Aid to Independent Living), Proceedings of the third TIDE Congress. [ 5] N. Katevas (Ed), Mobile robotics in health care services, IOS Press pp. 227251, Amsterdam, 2000. [ 6] G. Bolmsj, M. Olsson, P. Hedenborn, U. Lorentzon, F. Charnier, H. Nasri, Modular robotics design system integration of a robot for disabled people, Proceedings of the EU RISCON98, Athens, 1998. [ 7] Holly A. Yanco., Integrating robotic research: a survey of robotic wheelchair development, AAAI Spring Symposium on Integrating Robotic Research, Stanford, California, March 1998. [ 8] Warner, P.R and Prior, S.D. Investig ations into the design of a wheelchair mounted rehabilitation robotic manipulator, Proceedings of the 3rd Cambridge Workshop on Rehabilitation Robotics, Cambridge University, England, April 1994. [ 9] H.Eftring, K.Boschian, Technical results from manus user trials, Proc. ICORR 99, 136141, 1999

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57 [ 10] M. Hillman, A. Gammie, The Bath institute of medical engineering assistive robot, Proc. ICORR 94, 211212, 1994. [ 11] R. Alqasemi, E. McCaffrey, K. Edwards and R. Dubey, Analysis, Evaluation and Devel opment of Wheelchair Mounted Robotic Arms. Proceedings of the 2005 IEEE 9th International Conference on Rehabilitation Robotics, Chicago, IL, June 2005. [ 12] R. Alqasemi and R. Dubey. Maximizing Manipulation Capabilities for People with Disabilities Usi ng a 9DoF Wheelchair Mounted Robotic Arm System. Proceedings of the 2007 IEEE 10th International Conference on Rehabilitation Robotics. [ 13] K. Edwards, R. Alqasemi and R. Dubey, Wheelchair Mounted Robotic Arms: Design and Development, The First IEEE /RAS EMBS International Conference on Biomedical Robotics and Biomechatronics 2006. [ 14] R. Alqasemi, S. Mahler, R. Dubey, Design and construction of a robotic gripper for activities of daily living for people with disabilities, Proceedings of the 2007 ICORR, Noordwijk, the Netherlands, June 13 15, 2007. [ 15] A. Albu Schffer et al. From Torque FeedbackControlled Lightweight Robots to Intrinsically Compliant Systems. IEEE Robotics & Automation Magazine, September 2008. P.2030. [ 16] Herzinger, G., S porer, N., Albu Schaffer, A., Hahnle, M., Krenn, R., Pascucci, A., & Schedl, M. (2002). DLRs Torque Controlled Lightweight Robot III Are We Reaching the Technological Limits Now? Proceedings of the IEEE International Conference on Robotics & Automation. Pgs 17101716. [ 17] P. Shrock, F. Farelo, R. Alqasemi and R. Dubey. Design, Simulation and Testing of a New Modular Wheelchair Mounted Robotic Arm to Perform Activities of Daily Living Proceedings of the 2009 IEEE 11th International Conference on Rehabilitation Robotics [ 18] C. Ding, P. Duan, M. Zhang and H. Liu. The Kinematics of a Redundant Mobile Manipulator, Proceedings of the IEEE International Conference on Automation and Logistics 2009.

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58 [ 19] A. Luca, G. Oriolo, and P. Giordano, Kinematic Modeling and Redundancy Resolution for Nonholonomic Mobile Manipulators, Proceedings of the 2006 IEEE International Conference on Robotics and Automation (ICRA), pp. 18671873. [ 20] R. Zapata, JB. Thevenon, M. Perrier, E. Pommier and E. Badi. Path Planning abd trajectory Planning for Nonholonomic Mobile Robots, IEE/RJS International Workshop on Intelligent Robot and Systems 1989 [ 21] O. Gal, Z. Shiller and E. Rimon. Efficient and Safe Online Motion planning ib Dynamic Environments, Proceedings of the 2009 IEEE International Conference on Robotics and Automation (ICRA). [ 22] G.D. white, R.M. Bhatt, C Pei Tang and V.N. Krovi. Experimental Evaluation of Dynamic redundancy resolution in a Nonholonomic wheeled Mobile Manipulator. IEE/ASME Transactions on Mechatronics Vol. 14, No 3. 2009 [ 23] T. Chan, and R. Dubey, A Weighted Least Norm Solution Based Scheme for Avoiding Joint Limits for Redundant Joint Manipulators, IEEE Robotics and Automation Transactions (R&A Transactions). V. 11, N. 2, pp. 286292, 1995. [ 24] R. Alqasemi. Maximizing Manipulation Capabilities for People with Disabilities Using a 9 DoF Wheelchair Mounted Robotic Arm System. Doctoral Dissertation. University of South Florida. Tam pa, 2007. [25] M Wada. An omnidirectional 4WD Mobile Platform for Wheelchair Applications. Proceedings of the 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics. [ 2 6] J. Savage et al. ViRbot: A System for the Operation of M obile Robots. Lecture Notes in Computer Science. Springer Berlin/ Heidelberg. Vol 5001. 512519, 2008. [ 2 7] J. Savage, M. Billinghurst, A. Holden, The Virbot: A virtual reality mobile robot driven with multimodal commands. Expert Systems with Applications 15. 413419, 1998.

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59 [ 2 8] The Mathworks. Virtual Reality Toolbox Users Guide. The Mathworks Inc. Versio n 4.0.1, 2006 [ 2 9] R. Paul, 1981, Robot Manipulators: Mathematics, Programming and Control, The MIT Press, ISBN 026216082X. [ 3 0] Craig, J., 2003, Introduction to robotics mechanics and control, third edition, AddisonWesley Publishing, ISBN 0201543613. [ 31] E. Papadopoulos, J. Poulakakis, Planning and model based control for mobile manipulators, Proceedings of the 2001 IROS, 2000 [ 32 Nakamura, Y., Advanced robotics: redundancy and optimization, AddisonWesley Publishing, 1991, ISBN 0201151987. [ 33] Yoshikawa, T., Foundations of robotics: analysis and control, MIT Press, 1990, ISBN 0262240289.

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60 Appendices

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61 Appendix A. Virtual Reality Modeling Language 9_WMRA #VRML V2.0 utf8 NavigationInfo { type "EXAMINE" speed 30 avatarSize [ 1, 0, 0 ] headlight TRUE } DEF WMRAROBOT Group { children[ Group { children [ DEF EXT_SETTINGS Group { children [ WorldInfo { title "Wheelchair Mounted Robotic Arm, By: Redwan Alqasemi, USF 2007"}, NavigationInfo { type "EXAMINE" avatarSize 180 visibilityLimit 200 speed 1000 }, Background { groundColor [ 0.8 0.7 0.1 0.8 0.7 0.1] groundAngle [1.57] skyColor [ 0 0 1 0 0.5 1 0 0.5 1 0.5 0.5 0.5 1 0.5 0] skyAngle [ 1 1.15 1.35 1.57] #topUrl "cloud.jpg" }, D EF DynamicView Transform { rotation 0 1 0 0 translation 0 0 0 children [ Viewpoint { description "a_start" position 2500 500 1800

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62 A ppendix A (Continued) orientation 0 1 0 0.8 jump FALSE }, Viewpoint { description "a_far" position 900 6000 200 orientation 0.601 0.547 0.582 2.172 jump FALSE }, Viewpoint { description "a_bkltup" position 1300 1600 1600 orientation 0.1 1 0.25 2.4 jump FALSE }, Viewpoint { description "a_bkltdn" position 1400 400 1800 orientation 0.025 1 0.037 2.4 jump FALSE }, Viewpoint { description "a_ftltup" position 1600 1800 1400 orientation 0.1 0.9 0.25 2.4 jump FALSE }, Viewpoint { description "a_ftltdn" position 1700 400 1600 orientation 0.031 1 0.052 2.4 jump FALSE }, Viewpoint { description "a_ftrtup" position 1600 1900 1500 orientation 0.4 0.5 0.14 0.85 jump FALSE }, Viewpoint { description "a_ftrtdn" position 1700 300 1900 orientation 0.191 1 0.075 0.615 jump FALSE }, Viewpoint { description "a_bkrtup" position 1700 1700 1700 orientation 0.25 0.5 0.12 1 jump FALSE }, Viewpoint { description "a_bkrtdn"

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63 Appendix A (Continued) position 1800 500 1900 orientation 0.116 1 0.021 0.818 jump FALSE }, Viewpoint { description "a_birdeye" position 1100 4900 1900 orientation 0.56 0.72 0.4 2.2 jump FALSE }, Viewpoint { description "a_top" position 200 3100 0 orientation 0.577 0.577 0.577 2.1 jump FALSE }, ]} Viewpoint { description "top" position 200 3100 0 orientation 0.577 0.577 0.577 2.1 jump FALSE }, Viewpoint { description "birdeye" position 1100 4900 1900 orientation 0.56 0 .72 0.4 2.2 jump FALSE }, Viewpoint { description "bkrtdn" position 1800 500 1900 orientation 0.116 1 0.021 0.818 jump FALSE }, Viewpoint { description "bkr t up" position 1700 1700 1700 orientation 0.25 0.5 0.12 1 jump FALSE }, Viewpoint { description "ftrtdn" position 1700 300 1900 orientation 0.191 1 0.075 0.615 jump FALSE }, Viewpoint { description "ftrtup" position 1600 1900 1500 orientation 0.4 0.5 0.14 0.85 jump FALSE },

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64 Appendix A (Continued) Viewpoint { description "ftltdn" position 1700 400 1600 orientation 0.031 1 0.052 2.4 jump FALSE }, Viewpoint { description "ftltup" position 1600 1800 1400 orientation 0.1 0.9 0.25 2.4 jump FALSE }, Viewpoint { description "bkltdn" position 1400 400 1800 orientation 0.025 1 0.037 2.4 jump FALSE }, Viewpoint { description "bkltup" position 1300 1600 1600 orientation 0.1 1 0.25 2.4 jump FALSE }, Viewpoint { description "far" position 900 6000 200 orientation 0.601 0.547 0.582 2.172 jump FALSE }, Viewpoint { description "start" position 2500 500 1800 orientation 0 1 0 0.8 jump FALSE }, DEF GROUND Transform { rotation 1 0 0 0 translation 0 0 0 children [ Shape { geometry Box { size 10000 1 10000 } appearance Appearance { texture ImageTexture { url "woodfloor2.jpg" repeatS TRUE repeatT TRUE } textureTransform TextureTransform { rotation 0 center 0 0 translation 0 0 scale 3 3 }}}]},

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65 Appendix A (Continued) ]} ]} # Transforming the wheelchair world coordinate system to the VR's world coordinate system: DEF World Transform { rotation 1 0 0 1.5707963 translation 0 0 0 children [ DEF Chair Transform { rotation 0 0 1 0 translation 440 230 168 children [ # DEF WCR SphereSensor {} # DEF WCT PlaneSensor { minPosition 400 0 maxPosition 400 0 } Group { children [Inline { url "0_Chair.wrl" } DEF LWheel Transform { rotation 0 1 0 0 translation 0 0 0 children [ # DEF LW CylinderSensor { diskAngle 0 minAngle 1.5707963 maxAngle 1.5707963 } Group { children [Inline { url "0_LWheel.wrl" }]}]} DEF RWheel Transform { rotation 0 1 0 0 translation 0 0 0 children [ # DEF RW CylinderSensor { diskAngle 0 minAngle 1.5707963 maxAngle 1.5707963 } Group { children [Inline { url "0_RWheel.wrl" }]}]} DEF ARM1 Transform { rotation 1 0 0 1.5707963 translation 440 220 139 children [ # DEF JOINT1 CylinderSensor { diskAngle 0 minAngle 1.5707963 maxAngle 1.5707963 } Group { children [Inline { url "1.wrl" } DEF ARM2 Transform { rotation 0 0 1 1.5707963 translation 0 42.69 75.1 children [ # DEF JOINT2 CylinderSensor { diskAngle 0 minAngle 1.5708 maxAngle 1.5708 }

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66 Appendix A (Continued) Group { children [Inline { url "2.wrl" } DEF ARM3 Transform { rotation 0 1 0 1.5707963 translation 1.73 75.08 42.7 children [ # DEF JOINT3 CylinderSensor { diskAngle 0 minAngle 3.1416 maxAngle 3.1416 } Group { children [Inline { url "3.wrl" } DEF ARM4 Transform { rotation 0 0 1 0 translation 2.92 42.64 75.08 children [ # DEF JOINT4 CylinderSensor { diskAngle 0 minAngle 3.1416 maxAngle 3.1416 } Group { children [Inline { url "4.wrl" } DEF ARM5 Transform { rotation 0 1 0 1.5707963 translation 11.45 74.85 423.58 children [ # DEF JOINT5 CylinderSensor { diskAngle 0 minAngle 3.1416 maxAngle 3.1416 } Group { children [Inline { url "5.wrl" } DEF ARM6 Transform { rotation 0 0 1 1.5707963 translation 2.17 45.99 75.1 children [ # DEF JOINT6 CylinderSensor { diskAngle 0 minAngle 3.1416 maxAngle 3.1416 } Group { children [Inline { url "6.wrl" } DEF ARM7 Transform { rotation 0 1 0 1.5707963 translation 2.92 61.52 161.49 children [ # DEF JOINT7 CylinderSensor { diskAngle 0 minAngle 1.5708 maxAngle 1.5708 } Group { children [Inline { url "7.wrl" } DEF ARM8 Transform { rotation 0 0 1 0 translation 1.78 61.39 192.29 children [

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67 Appendix A (Continued) # DEF JOINT8 CylinderSensor { diskAngle 0 minAngle 3.1416 maxAngle 3.1614 } Group { children [Inline { url "8.wrl" } ]}]} ]}]} ]}]} ]}]} ]}]} ]}]} ]}]} ]}]} ]}]} ]} # ROUTE WCT.translation_changed TO Chair.set_translation # ROUTE WCR.rotation_changed TO Chair.set_rotation # ROUTE LW.rotation_changed TO LWheel.set_rotation # ROUTE RW.rotation_changed TO RWheel.set_rotation # ROUTE JOINT1.rotation_changed TO ARM1.set_rotation # ROUTE JOINT2.rotation_changed TO ARM2.set_rotation # ROUTE JOINT3.rotation_changed TO ARM3.set_rotation # ROUTE JOINT4.rotation_changed TO ARM4.set_rotation # ROUTE JOINT5.rotation_changed TO ARM5.set_rotation # ROUTE JOINT6.rotation_changed TO ARM6.set_rotation # ROUTE JOINT7.rotation_changed TO ARM7.set_rotation # ROUTE JOINT8.rotation_changed TO ARM8.set_rotation ]} Box #VRML V2.0 utf8 Group { children [ Transform { translation 0 0 0 children [ DEF BOX Shape { appearance Appearance { material DEF _mat1 Material { ambientIntensity 0.2 diffuseColor 0.2 0.2 0 emissiveColor 0 0 0 shininess 0.2 specularColor 0 0 0 transparency 0 } } geometry Box { size 300 200 300} } ] } ] }

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68 Appendix A (Continued) Couch #VRML V2.0 utf8 #Created with VRealm Builder v2.0 #Integrated Data Systems Inc. #www.idsnet.com Group { children [ NavigationInfo { } Transform { scale 60 60 60 children [ Group { children Transform { translation 8 2 4 children [ Shape { appearance Appearance { material DEF _mat1 Material { ambientIntensity 0.2 diffuseColor 0.1 0.4 0.5 } texture ImageTexture { url "texture/leather_white.jpg" } } geometry Sphere { radius 1 } } Transform { translation 0 0 4 rotation 1 0 0 1.57 children Shape { appearance Appearance { material USE _mat1 texture ImageTexture { url "texture/leather_white.jpg"

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69 Appendix A (Continued) } } geometry Cylinder { height 8 radius 1 } } } ] } } Group { children Transform { translation 8 2 4 children [ Shape { appearance Appearance { material USE _mat1 texture ImageTexture { url "texture/leather_white.jpg" } } geometry Sphere { radius 1 } } Transform { translation 0 0 4 rotation 1 0 0 1.57 children Shape { appearance Appearance { material USE _mat1 texture ImageTexture { url "texture/leather_white.jpg" } } geometry Cylinder { height 8 radius 1 }

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70 Appendix A (Continued) } } ] } } Group { children Transform { translation 7.5 1.5 0 children [ Shape { appearance Appearance { material USE _mat1 texture ImageTexture { url "texture/leather_white.jpg" } } geometry Box { size 1 7 8 } } Transform { translation 15 0 0 children Shape { appearance Appearance { material USE _mat1 texture ImageTexture { url "texture/leather_white.jpg" } } geometry Box { size 1 7 8 } } } ] } } Group { children Transform { translation 0 3.5 0 children Shape { appearance Appearance {

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71 Appendix A (Continued) material USE _mat1 texture ImageTexture { url "texture/leather_white.jpg" } } geometry Box { size 14 3 8 } } } } Group { children Transform { translation 0 1.5 3.5 children [ Shape { appearance Appearance { material USE _mat1 texture ImageTexture { url "texture/leather_white.jpg" } } geometry Box { size 15 7 1 } } Transform { translation 7.5 3.5 0.5 children [ Shape { appearance Appearance { material USE _mat1 texture ImageTexture { url "texture/leather_white.jpg" } } geometry Sphere { radius 1 } }

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72 Appendix A (Continued) Transform { translation 15 0 0 children [ Shape { appearance Appearance { material USE _mat1 texture ImageTexture { url "texture/leather_white.jpg" } } geometry Sphere { radius 1 } } Transform { translation 7.5 0 0 rotation 0 0 1 1.57 children Shape { appearance Appearance { material USE _mat1 texture ImageTexture { url "texture/leather_white.jpg" } } geometry Cylinder { height 15 radius 1 } } } ] } ] } ] } } Group { children Transform { translation 0 1 0 children [

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73 Appendix A (Continued) Shape { appearance Appearance { material USE _mat1 texture ImageTexture { url "texture/leather_white.jpg" } } geometry Box { size 14 2 6 } } Transform { translation 0 0 3 rotation 0 0 1 1.57 children Shape { appearance Appearance { material USE _mat1 texture ImageTexture { url "texture/leather_white.jpg" } } geometry Cylinder { height 15 radius 1 } } } ] } } ] } ] }

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74 Appendix A (Continued) Door #VRML V1.0 ascii Separator { MaterialBinding { value OVERALL } Material { ambientColor [ 0.796078 0.823529 0.937255 ] diffuseColor [ 0.796078 0.823529 0.937255 ] emissiveColor [ 0.063686 0.065882 0.074980 ] specularColor [ 0.756275 0.782353 0.890392 ] shininess [ 0.550000 ] transparency [ 0.000000 ] } Coordinate3 { point [ 0.000000 0.000000 0.000000, 0.000000 0.000000 2.200000, 0.000000 0.010000 0.000000, 0.000000 0.010000 2.200000, 0.900000 0.000000 0.000000, 0.900000 0.000000 2.200000, 0.900000 0.010000 0.000000, 0.900000 0.010000 2.200000 ] } IndexedFaceSet { coordIndex [ 2, 6, 0, 1, 0, 6, 4, 1, 3, 2, 1, 1, 1, 2, 0, 1, 7, 3, 5, 1, 5, 3, 1, 1, 6, 7, 4, 1, 4, 7, 5, 1, 3, 7, 2, 1, 2, 7, 6, 1, 5, 1, 4, 1, 4, 1, 0, 1 ] } }

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75 Appendix A (Continued) Laser #VRML V2.0 utf8 #Created with VRealm Builder v2.0 #Integrated Data Systems Inc. #www.idsnet.com Transform { scale 60 60 60 translation 0 0 0 rotation 1 0 0 3.141592 children Shape { appearance Appearance { material DEF _mat1 Material { ambientIntensity 0.2 diffuseColor 0 0 0 emissiveColor 1 0 0 shininess 0.2 specularColor 0 0 0 transparency 0 } } geometry Cone { bottomRadius 0.05 height 3.8 } } } Laser Mount #VRML V2.0 utf8 #Created with VRealm Builder v2.0 #Integrated Data Systems Inc. #www.idsnet.com Transform { translation 9.53674e007 3.21865e006 0 children Shape { appearance Appearance { material Material { }

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76 Appendix A (Continued) texture DEF Metal ImageTexture { url "texture/Metal.jpg" } } geometry Box { size 20 20 20 } } } Shelf #VRML V2.0 utf8 #Created with VRealm Builder v2.0 #Integrated Data Systems Inc. #www.idsnet.com Transform { translation 110.317 144.058 153.659 rotation 0.173679 0.966449 0.189238 0.0127889 scale 799.999 799.999 799.999 children Shape { appearance Appearance { material Material { ambientIntensity 1 diffuseColor 0.668235 0.564706 0.404706 emissiveColor 0.167059 0.141176 0.101176 shininess 0.31 specularColor 0.668235 0.564706 0.404706 } texture DEF Wood_Tan ImageTexture { url "texture/Wood_6.gif" } } geometry IndexedFaceSet { color Color { color 0.835294 0.705882 0.505882 } coord Coordinate { point [ 0.044476 0.045526 0.02, 0.044476 0.045526 0.4,

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77 Appendix A (Continued) 0.044476 1.75447 0.02, 0.044476 1.75447 0.4, 0.016654 0.023677 0, 0.016654 0.023677 0.4, 0.016654 0.393539 0, 0.016654 0.393539 0.4, 0.016654 0.413539 0, 0.016654 0.413539 0.4, 0.016654 0.908174 0, 0.016654 0.908174 0.4, 0.016654 0.928174 0, 0.016654 0.928174 0.4, 0.016654 1.35288 0, 0.016654 1.35288 0.4, 0.016654 1.37288 0, 0.016654 1.37288 0.4, 0.016654 1.73632 0, 0.016654 1.73632 0.4, 0.927702 0.023677 0, 0.927702 0.023677 0.4, 0.927702 0.393539 0, 0.927702 0.393539 0.4, 0.927702 0.413539 0, 0.927702 0.413539 0.4, 0.927702 0.908174 0, 0.927702 0.908174 0.4, 0.927702 0.928174 0, 0.927702 0.928174 0.4, 0.927702 1.35288 0, 0.927702 1.35288 0.4, 0.927702 1.37288 0, 0.927702 1.37288 0.4, 0.927702 1.73632 0, 0.927702 1.73632 0.4, 0.955524 0.045526 0.02, 0.955524 0.045526 0.4, 0.955524 1.75447 0.02, 0.955524 1.75447 0.4 ] } normal Normal { vector [ 1 0 0, 0 1 0, 0 0 1, 0 0 1, 0 1 0, 1 0 0 ] } colorPerVertex FALSE normalPerVertex TRUE coordIndex [ 7, 3, 5, 1, 5, 3, 1, 1,

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78 Appendix A (Continued) 5, 1, 21, 1, 21, 1, 37, 1, 21, 37, 23, 1, 13, 15, 3, 1, 29, 13, 11, 1, 11, 13, 3, 1, 11, 3, 9, 1, 9, 3, 7, 1, 9, 7, 25, 1, 3, 35, 39, 1, 39, 35, 33, 1, 7, 23, 25, 1, 25, 23, 37, 1, 25, 37, 27, 1, 27, 37, 39, 1, 11, 27, 29, 1, 29, 27, 39, 1, 29, 39, 31, 1, 31, 39, 33, 1, 31, 33, 15, 1, 15, 33, 17, 1, 15, 17, 3, 1, 3, 17, 19, 1, 3, 19, 35, 1, 0, 1, 2, 1, 2, 1, 3, 1, 36, 37, 0, 1, 0, 37, 1, 1, 38, 39, 36, 1, 36, 39, 37, 1, 2, 3, 38, 1, 38, 3, 39, 1, 19, 17, 18, 1, 18, 17, 16, 1, 17, 33, 16, 1, 16, 33, 32, 1, 33, 35, 32, 1, 32, 35, 34, 1, 35, 19, 34, 1, 34, 19, 18, 1, 21, 23, 20, 1, 20, 23, 22, 1, 23, 7, 22, 1, 22, 7, 6, 1, 7, 5, 6, 1, 6, 5, 4, 1, 5, 21, 4, 1, 4, 21, 20, 1, 25, 27, 24, 1, 24, 27, 26, 1, 27, 11, 26, 1, 26, 11, 10, 1 11, 9, 10, 1, 10, 9, 8, 1, 9, 25, 8, 1, 8, 25, 24, 1, 15, 13, 14, 1, 14, 13, 12, 1, 13, 29, 12, 1, 12, 29, 28, 1, 29, 31, 28, 1, 28, 31, 30, 1, 31, 15, 30, 1, 30, 15, 14, 1, 28, 30, 12, 1, 12, 30, 14, 1, 10, 8, 26, 1, 26, 8, 24, 1, 6, 4, 22, 1, 22, 4, 20, 1, 32, 34, 16, 1, 16, 34, 18, 1, 0, 2, 36, 1, 36, 2, 38, 1 ] normalIndex [ 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,

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79 Appendix A (Continued) 5, 5, 5, 1, 5, 5, 5, 1, 4, 4, 4, 1, 4, 4, 4, 1, 5, 5, 5, 1, 5, 5, 5, 1, 4, 4, 4, 1, 4, 4, 4, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 1, 5, 5, 5, 1, 4, 4, 4, 1, 4, 4, 4, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 1, 5, 5, 5, 1, 4, 4, 4, 1, 4, 4, 4, 1, 5, 5, 5, 1, 5, 5, 5, 1, 4, 4, 4, 1, 4, 4, 4, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 2, 2, 2, 1, 2, 2, 2, 1 ] } } } Sink Door #VRML V2.0 utf8 #Created with VRealm Builder v2.0 #Integrated Data Systems Inc. #www.idsnet.com Transform { scale 800 800 800 children Shape { appearance Appearance { material Material { ambientIntensity 1 diffuseColor 0.721569 0.646275 0.404706 emissiveColor 0.180392 0.161569 0.101176 shininess 0.31 specularColor 0.721569 0.646275 0.404706

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80 Appendix A (Continued) } texture DEF Wood_Tan ImageTexture { url "texture/Wood_6.gif" } } geometry IndexedFaceSet { color Color { color 0.901961 0.807843 0.505882 } coord Coordinate { point [ 0 0 0, 0 0 0.02, 0 1 0, 0 1 0.02, 0.553993 0.46 0.02, 0.553993 0.46 0.05, 0.553993 0.47 0.02, 0.553993 0.47 0.04, 0.553993 0.51 0.02, 0.553993 0.51 0.04, 0.553993 0.52 0.02, 0.553993 0.52 0.05, 0.563994 0.46 0.02, 0.563994 0.46 0.05, 0.563994 0.47 0.02, 0.563994 0.47 0.04, 0.563994 0.51 0.02, 0.563994 0.51 0.04, 0.563994 0.52 0.02, 0.563994 0.52 0.05, 0.6 0 0, 0.6 0 0.02, 0.6 1 0, 0.6 1 0.02 ] } normal Normal { vector [ 1 0 0, 0 1 0, 0 0 1, 0 0 1, 0 1 0, 1 0 0 ] } colorPerVertex FALSE normalPerVertex TRUE

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81 Appendix A (Continued) coordIndex [ 18, 23, 10, 1, 10, 23, 3, 1, 10, 3, 8, 1, 6, 14, 16, 1, 16, 8, 6, 1, 6, 8, 3, 1, 6, 3, 4, 1, 4, 3, 1, 1, 4, 1, 12, 1, 12, 1, 21, 1, 12, 21, 14, 1, 14, 21, 23, 1, 14, 23, 16, 1, 16, 23, 18, 1, 1, 3, 0, 1, 0, 3, 2, 1, 21, 1, 20, 1, 20, 1, 0, 1, 23, 21, 22, 1, 22, 21, 20, 1, 3, 23, 2, 1, 2, 23, 22, 1, 22, 20, 2, 1, 2, 20, 0, 1, 6, 4, 7, 1, 7, 4, 5, 1, 7, 5, 9, 1, 9, 5, 11, 1, 9, 11, 8, 1, 8, 11, 10, 1, 13, 5, 12, 1, 12, 5, 4, 1, 16, 18, 17, 1, 17, 18, 19, 1, 17, 19, 15, 1, 15, 19, 13, 1, 15, 13, 14, 1, 14, 13, 12, 1, 7, 15, 6, 1, 6, 15, 14, 1, 11, 19, 10, 1, 10, 19, 18, 1, 17, 9, 16, 1, 16, 9, 8, 1, 7, 9, 15, 1, 15, 9, 17, 1, 13, 19, 5, 1, 5, 19, 11, 1 ] normalIndex [ 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 1, 5, 5, 5, 1, 4, 4, 4, 1, 4, 4, 4, 1, 2, 2, 2, 1, 2, 2, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 1, 5, 5, 5, 1, 5, 5, 5, 1, 5, 5, 5, 1, 5, 5, 5, 1, 5, 5, 5, 1, 4, 4, 4, 1, 4, 4, 4, 1, 4, 4, 4, 1, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 3, 3, 3, 1, 3, 3, 3, 1 ] } } }

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82 Appendix A (Continued) Table #VRML V2.0 utf8 #Created with VRealm Builder v2.0 #Integrated Data Systems Inc. #www.idsnet.com Group { children [ NavigationInfo { } Transform { scale 60 60 60 children [ Shape { appearance Appearance { material DEF _mat1 Material { ambientIntensity 0.2 diffuseColor 0.25 0.15 0.1 emissiveColor 0 0 0 shininess 0.2 specularColor 0 0 0 transparency 0 } texture DEF Wood_Brown ImageTexture { url "texture/Wood_5.jpg" } } geometry Cylinder { height 0.5 radius 8 } } ]} Transform {

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83 Appendix A (Continued) translation 0 1 0 scale 60 60 60 children [ Shape { appearance Appearance { material USE _mat1 texture DEF Wood_Brown ImageTexture { url "texture/Wood_5.jpg" } } geometry Cylinder { height 1 radius 1 } } Transform { translation 0 0.5 0 children [ Shape { appearance Appearance { material USE _mat1 texture DEF Wood_Brown ImageTexture { url "texture/Wood_5.jpg" } } geometry Sphere { radius 1 } } Transform { translation 0 1.5 0 children [ Shape { appearance Appearance { material USE _mat1 texture DEF Wood_Brown ImageTexture { url "texture/Wood_5.jpg" } }

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84 Appendix A (Continued) geometry Sphere { radius 1 } } Transform { translation 0 1.5 0 children [ Shape { appearance Appearance { material USE _mat1 texture DEF Wood_Brown ImageTexture { url "texture/Wood_5.jpg" } } geometry Sphere { radius 1 } } Transform { translation 0 1.5 0 children [ Shape { appearance Appearance { material USE _mat1 texture DEF Wood_Brown ImageTexture { url "texture/Wood_5.jpg" } } geometry Sphere { radius 1 } } Transform { translation 0 1.5 0

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85 Appendix A (Continued) children [ Shape { appearance Appearance { material USE _mat1 texture DEF Wood_Brown ImageTexture { url "texture/Wood_5.jpg" } } geometry Cylinder { height 3 radius 1 } } Transform { translation 0 1 0 children [ Shape { appearance Appearance { material USE _mat1 texture DEF Wood_Brown ImageTexture { url "texture/Wood_5.jpg" } } geometry Cone { bottomRadius 2 height 3 } } Transform { translation 0 1 0 children [ Shape { appearance Appearance {

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86 Appendix A (Continued) material USE _mat1 texture DEF Wood_Brown ImageTexture { url "texture/Wood_5.jpg" } } geometry Cone { bottomRadius 4 height 1.5 } } Transform { translation 0 0.75 0 children Shape { appearance Appearance { material USE _mat1 texture DEF Wood_Brown ImageTexture { url "texture/Wood_5.jpg" } } geometry Cylinder { height 0.25 radius 5.5 } } } ] } ]

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87 Appendix A (Continued) } ] } ] } ] } ] } ] } ] } ] } Wall #VRML V2.0 utf8 #Created with VRealm Builder v2.0 #Integrated Data Systems Inc. #www.idsnet.com Collision { children [] } Group { children [ NavigationInfo { } Transform { translation 1.5 0 0 children Transform { scale 201 201 201 children Shape { appearance Appearance { material Material { ambientIntensity 1 diffuseColor 0.9 0.767329 0.619635 shininess 1 } texture NULL } geometry Box {

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88 Appendix A (Continued) size 14.8 7.1 0.25 } } } } ] }

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89 Appendix B. Matlab Functions WMRA_final_orientation % This function simulates the wmra final orientation acording to the needs % of the task. the final angle to be rotated is an input % Function Declaration: function WMRA_final_orientation(ini, vr, ml, arm, Tiwc, qi,ang) % Closing the Arm library and Matlab Graphics Animation and Virtual Reality Animation and Plots windows: if ini==3 if arm==1 try WMRA_ARM_Motion(ini, 0, 0, 0); end end if vr==1 try WMRA_VR_Animation2(ini, 0, 0); end end if ml==1 try WMRA_ML_Animation2(ini, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0); end end return; end % Defining the used conditions: qd=qi(1:7);% Final joint angles %qd=[pi/2;pi/2;0;pi/2;pi/2;pi/2;0]; % Final joint angles (Ready Position). ts=10; % (5 or 10 or 20) Simulation time to move the arm from any position to the ready position. n=100; % Number of time steps. dt=ts/n; % The time step to move the arm from any position to the ready position. dqw=(ang)/(0.5*n+5); %dq=(qdqi(1:7))/(0.5*n+5); % Initializing the physical Arm: if arm==1 WMRA_ARM_Motion(ini, 2, [qi;0], dt); ddt=0; end % Initializing Virtual Reality Animation:

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Appendix B (continued) 90 if vr==1 WMRA_VR_Animation2(ini, Tiwc, qi); end % Initializing Robot Animation in Matlab Graphics: if ml==1 % Inputting the DH Parameters in a Matrix form: DH=WMRA_DH(qi); % Calculating the transformation matrices of each link: T01=WMRA_rotx(DH(1,1))*WMRA_transl(DH(1,2),0,0)*WMRA_rotz(DH(1,4))*WMRA _transl(0,0,DH(1,3)); T12=WMRA_rotx(DH(2,1))*WMRA_transl(DH(2,2),0,0)*WMRA_rotz(DH(2,4))*WMRA _transl(0,0,DH(2,3)); T23=WMRA_rotx(DH(3,1))*WMRA_transl(DH(3,2),0,0)*WMRA_rotz(DH(3,4))*WMRA _transl(0,0,DH(3,3)); T34=WMRA_rotx(DH(4,1))*WMRA_transl(DH(4,2),0,0)*WMRA_rotz(DH(4,4))*WMRA _transl(0,0,DH(4,3)); T45=WMRA_rotx(DH(5,1))*WMRA_transl(DH(5,2),0,0)*WMRA_rotz(DH(5,4))*WMRA _transl(0,0,DH(5,3)); T56=WMRA_rotx(DH(6,1))*WMRA_transl(DH(6,2),0,0)*WMRA_rotz(DH(6,4))*WMRA _transl(0,0,DH(6,3)); T67=WMRA_rotx(DH(7,1))*WMRA_transl(DH(7,2),0,0)*WMRA_rotz(DH(7,4))*WMRA _transl(0,0,DH(7,3)); % Calculating the Transformation Matrix of the initial and desired arm positions: Ti=Tiwc*T01*T12*T23*T34*T45*T56*T67; Td=Tiwc*WMRA_q2T(qd); WMRA_ML_Animation2(ini, Ti, Td, Tiwc, T01, T12, T23, T34, T45, T56, T67); end % Check for the shortest route: diff=qdqi(1:7); for i =1:7 if diff(i) > pi diff(i)=diff(i)2*pi; elseif diff(i) < (pi) diff(i)=diff(i)+2*pi; end end % Joint angle change at every time step. dq=[diff/n;0;0];

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Appendix B (continued) 91 % Initialization: qo=qi; tt=0; while tt <= (tsdt) % Starting a timer: tic; % Calculating the new Joint Angles: qn=qo+dq; % Updating the physical Arm: if arm==1 ddt=ddt+dt; if ddt>=0.5 || tt>=(tsdt) WMRA_ARM_Motion(2, 1, [qn;0], ddt); ddt=0; end end % Updating Virtual Reality Animation: if vr==1 WMRA_VR_Animation2(2, Tiwc, qn); end % Updating Matlab Animation: if ml==1 % Calculating the new Transformation Matrix: T1a=WMRA_rotx(DH(1,1))*WMRA_transl(DH(1,2),0,0)*WMRA_rotz(qn(1))*WMRA_t ransl(0,0,DH(1,3)); T2a=WMRA_rotx(DH(2,1))*WMRA_transl(DH(2,2),0,0)*WMRA_rotz(qn(2))*WMRA_t ransl(0,0,DH(2,3)); T3a=WMRA_rotx(DH(3,1))*WMRA_transl(DH(3,2),0,0)*WMRA_rotz(qn(3))*WMRA_t ransl(0,0,DH(3,3)); T4a=WMRA_rotx(DH(4,1))*WMRA_transl(DH(4,2),0,0)*WMRA_rotz(qn(4))*WMRA_t ransl(0,0,DH(4,3)); T5a=WMRA_rotx(DH(5,1))*WMRA_transl(DH(5,2),0,0)*WMRA_rotz(qn(5))*WMRA_t ransl(0,0,DH(5,3)); T6a=WMRA_rotx(DH(6,1))*WMRA_transl(DH(6,2),0,0)*WMRA_rotz(qn(6))*WMRA_t ransl(0,0,DH(6,3)); T7a=WMRA_rotx(DH(7,1))*WMRA_transl(DH(7,2),0,0)*WMRA_rotz(qn(7))*WMRA_t ransl(0,0,DH(7,3));

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Appendix B (continued) 92 WMRA_ML_Animation(2, Ti, Td, Tiwc, T1a, T2a, T3a, T4a, T5a, T6a, T7a); end % Updating the old values with the new values for the next iteration: Tiwc=Tiwc*WMRA_rotz(dqw); qn(9)=qn(9)+dqw; qo=qn; tt=tt+dt; % Pausing for the speed sync: pause(dttoc); end WMRA_Main_Both % This is a simplified version of the Main program to acomplish a subtask % with motion control. most of the options are prespecified and will not be % changed by the user % Declaring the global variables to be used for the touch screen control: global VAR_DX global VAR_SCREENOPN global dHo % Defining used parameters: d2r=pi/180; % Conversions from Degrees to Radians. r2d=180/pi; % Conversions from Radians to Degrees. % Reading the Wheelchair's constant dimentions, all dimentions are converted in millimeters: L=WMRA_WCD; radi=1000; e=1; % User input prompts: %choice000 = input('\ n Choose what to control: \ n For combined Wheelchair and Arm control, press "1", \ n For Arm only control, press "2", \ n For Wheelchair only control, press "3". \ n','s'); choice000 = 1; WCA=1; %choice00000 = input('\ n Choose whose frame to base the control on: \ n For Ground Frame, press "1", \ n For Wheelchair Frame, press "2", \ n For Gripper Frame, press "3". \ n','s'); choice00000=1;

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Appendix B (continued) 93 coord=1; %choice0000 = input('\ n Choose the cartesian coordinates to be controlled: \ n For Position and Orientation, press "1", \ n For Position only, press "2". \ n','s'); choice0000 =1; cart=1; %choice5 = input('\ n Please enter the desired optimization method: (1= SRI & WLN, 2= PI & WLN, 3= SRI & ENE, 4= PI & ENE) \ n','s'); choice5 =1; optim=1; %choice50 = input('\ n Do you want to include Joint Limit Avoidance? (1= Yes, 2= No) \ n','s'); choice50 =1; JLA=1; %choice500 = input('\ n Do you want to include Joint Limit/Velocity and Obstacle Safety Stop? (1= Yes, 2= No) \ n','s'); choice500 = 1; JLO=1; %choice0 = input('\ n Choose the control mode: \ n For circle control, press "6", \ n For position control, press "1", \ n For velocity control, press "2", \ n For SpaceBall control, press "3", \ n For Psychology Mask control, press "4", \ n For Touch Screen control, press "5",\ n For Switch, press "7". \ n','s'); choice0 ='1'; if choice0=='1' cont=1; %Td = input('\ n Please enter the transformation matrix of the desired position and orientation from the controlbased frame \ n (e.g. [0 0 1 1455;1 0 0 369;0 1 0 999; 0 0 0 1]) \ n'); %Td=[0 0 1 1955;1 0 0 3000;0 1 0 800; 0 0 0 1]*WMRA_rotx(90)*WMRA_roty(70); Td=[0 0 1 1955;1 0 0 1169;0 1 0 999; 0 0 0 1] *WMRA_rotx(pi/6)*WMRA_roty(pi/4); %v = input('\ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); v=50; %choice00 = input('\ n Chose the Trajectory generation function: \ n Press "1" for a Polynomial function with Blending, or \ n press "2" for a Polynomial function without Blending, or \ n press "3" for a Linear function.\ n','s'); choice00=1; trajf=1; elseif choice0=='7' cont=1; Td = [0 0 1 1455;1 0 0 369;0 1 0 999; 0 0 0 1]; v = input(' \ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); choice00 = input(' \ n Chose the Trajectory generation function: \ n Press "1" for a Polynomial function with Blending, or \ n press "2" for a Polynomial function without Blending, or \ n press "3" for a Linear function.\ n', 's'); if choice00=='2' trajf=2;

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Appendix B (continued) 94 elseif choice00=='3' trajf=3; else trajf=1; end elseif choice0=='2' cont=2; ts = input(' \ n Please enter the desired simulation time in seconds (e.g. 2) \ n'); if cart==2 Vd = input(' \ n Please enter the desired 3x1 cartesian velocity vector of the gripper (in mm/s) (e.g. [70;70;70]) \ n'); else Vd = input(' \ n Please enter the desired 6x1 cartesian velocity vector of the gripper (in mm/s, radians/s) (e.g. [70;70;70;0.001;0.001;0.001]) \ n'); end elseif choice0=='3' cont=3; % Space Ball will be used for control. v = input(' \ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); elseif choice0=='4' cont=4; % BCI 2000 Psychology Mask will be used for control. v = input(' \ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); port1 = input(' \ n Please enter the desired port number (e.g. 19711) \ n'); choice00 = input(' \ n Chose the Trajectory generation function: \ n Press "1" for a Polynomial function with Blending, or \ n press "2" for a Polynomial function without Blending, or \ n press "3" for a Linear function, or \ n press "4" for a Circular Polynomial function with Blending. \ n', 's'); elseif choice0=='6' choice0=6; cont=6; %radi = input('\ n Please enter the radius of the cirle in mm (e.g. 1000) \ n'); radi=1000; %e = input('\ n If the door opens to the left press "1".\ n If it opens to the right press "2" \ n'); e=2; %v = input('\ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); v=50; trajf=4; else cont=5; % Touch Screen will be used for control. v = input(' \ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); end

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Appendix B (continued) 95 choice1 = input(' \ n Choose animation type or no animation: \ n For Virtual Reality Animation, press "1", \ n For Matlab Graphics Animation, press "2", \ n For BOTH Animations, press "3", \ n For NO Animation, press "4". \ n', 's'); if choice1=='2' vr = 0; ml = 1; elseif choice1=='3' vr = 1; ml = 1; elseif choice1=='4' vr = 0; ml = 0; else vr = 1; ml = 0; end %choice10 = input('\ n Would you like to run the actual WMRA? \ n For yes, press "1", \ n For no, press "2". \ n','s'); choice10='2'; if choice10=='1' arm=1; else arm=0; end %choice2 = input('\ n Press "1" if you want to start at the "ready" position, \ n or press "2" if you want to enter the initial joint angles. \ n','s'); choice2='1'; if choice2=='2' qi = input(' \ n Please enter the arms initial angles vector in radians (e.g. [pi/2;pi/2;0;pi/2;pi/2;pi/2;0]) \ n'); WCi = input(' \ n Please enter the initial x,y position and z orientation of the WMRA base from the ground base in millimeters and radians (e.g. [200;500;0.3]) \ n'); ini=0; else qi=[90;90;0;90;90;90;0]*d2r; WCi=[0;0;0]; ini=0; if vr==1 || ml==1 || arm==1 %choice3 = input('\ n Press "1" if you want to include "park" to "ready" motion, \ n or press "2" if not. \ n','s'); choice3= '1'; if choice3=='2' ini=0; else ini=1; end end end %choice4 = input('\ n Press "1" if you do NOT want to plot the simulation results, \ n or press "2" if do. \ n','s'); choice4 ='2'; if choice4=='2'

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Appendix B (continued) 96 plt=2; else plt=1; end % Calculating the Transformation Matrix of the initial position of the WMRA's base: Tiwc=WMRA_p2T(WCi(1),WCi(2),WCi(3)); % Calculating the initial Wheelchair Variables: qiwc=[sqrt(WCi(1)^2+WCi(2)^2);WCi(3)]; % Calculating the initial transformation matrices: [Ti, Tia, Tiwc, T01, T12, T23, T34, T45, T56, T67]=WMRA_Tall(1, qi, [0;0], Tiwc); if cont==1 % Calculating the linear distance from the initial position to the desired position and the linear velocity: if coord==2 D=sqrt( (Td(1,4)Tia(1,4))^2 + (Td(2,4)Tia(2,4))^2 + (Td(3,4)Tia(3,4))^2); elseif coord==3 D=sqrt( (Td(1,4))^2 + (Td(2,4))^2 + (Td(3,4))^2); else D=sqrt( (Td(1,4)Ti(1,4))^2 + (Td(2,4)Ti(2,4))^2 + (Td(3,4)Ti(3,4))^2); end % Calculating the number of iteration and the time increment (delta t) if the linear step increment of the tip is 1 mm: dt=0.05; % Time increment in seconds. total_time=D/v; % Total time of animation. n=round(total_time/dt); % Number of iterations rounded up. dt=total_time/n; % Adjusted time increment in seconds. % Calculating the Trajectory of the end effector, and once the trajectory is calculated, we should redefine "Td" based on the ground frame: if coord==2 Tt=WMRA_traj(radi,trajf, Tia, Td, n+1); Td=Tiwc*Td; elseif coord==3 Tt=WMRA_traj(radi,trajf, eye(4), Td, n+1); Td=Ti*Td; else Tt=WMRA_traj(radi,trajf, Ti, Td, n+1); end elseif cont==2 % Calculating the number of iterations and the time increment (delta t) if the linear step increment of the gripper is 1 mm: dt=0.05; % Time increment in seconds. total_time=ts; % Total time of animation. n=round(total_time/dt); % Number of iterations rounded up.

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Appendix B (continued) 97 dt=total_time/n; % Adjusted time increment in seconds. dx=Vd*dt; Td=Ti; elseif cont==3 WMRA_exit(); % This is to stop the simulation in SpaceBall control when the user presses the exit key. dt=0.05; dx=v*dt*[spdata1(3)/20 ; spdata1(1)/40 ; spdata1(2)/30 ; spdata1(6)/1500 ; spdata1(4)/900 ; spdata1(5)/1300]; dg=spdata1(7); Td=Ti; n=1; elseif cont==4 WMRA_exit(); % This is to stop the simulation in Psychology Mask control when the user presses the exit key. dt=0.05; dx=v*dt*WMRA_psy(port1); dg=dx(7); dx=dx(1:6); Td=Ti; n=1; elseif cont==6 % Calculating the desired transformation matrix based on the radius: Tdoor=Ti; Tdoor(1,4)=Ti(1,4)+radi/2; Tdoor(2,4)=Ti(2,4)+radi/2; Td=Tdoor; Td(1,4)=Td(1,4)radi; Td(2,4)=Td(2,4)((1)^e)*radi; % Calculating the circular distance from the initial position to the desired position and the linear velocity: D=0.5*pi*radi; % Calculating the number of iteration and the time increment (delta t) if the linear step increment of the tip is 1 mm: dt=0.05; % Time increment in seconds. total_time=D/v; % Total time of animation. n=round(total_time/dt); % Number of iterations rounded up. dt=total_time/n; % Adjusted time increment in seconds. % Calculating the Trajectory of the end effector, and once the trajectory is calculated, we should redefine "Td" based on the ground frame: if coord==2 Tt=WMRA_traj(radi,trajf, Tia, Td, n+1,e); Td=Tiwc*Td; elseif coord==3 Tt=WMRA_traj(radi,trajf, eye(4), Td, n+1,e); Td=Ti*Td; else Tt=WMRA_traj(radi,trajf, Ti, Td, n+1,e); end else

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Appendix B (continued) 98 WMRA_screen('0'); % This is to start the screen controls. Argument: '0'=BACK button disabled, '1'=BACK button enabled. dt=0.05; dx=v*dt*VAR_DX(1:6); dg=VAR_DX(7); Td=Ti; n=1; end % Initializing the joint angles, the Transformation Matrix, and time: dq=zeros(9,1); dg=0; qo=[qi;qiwc]; To=Ti; Toa=Tia; Towc=Tiwc; tt=0; i=1; dHo=[0;0;0;0;0;0;0]; % Initializing the WMRA: if ini==0 % When no "park" to "ready" motion required. % Initializing Virtual Reality Animation: if vr==1 WMRA_VR_Animation(1, Towc, qo); end % Initializing Robot Animation in Matlab Graphics: if ml==1 WMRA_ML_Animation(1, To, Td, Towc, T01, T12, T23, T34, T45, T56, T67); end % Initializing the Physical Arm: if arm==1 WMRA_ARM_Motion(1, 2, [qo;dg], 0); ddt=0; end elseif ini==1 && (vr==1 || ml==1 || arm==1) % When "park" to "ready" motion is required. WMRA_park2ready(1, vr, ml, arm, Towc, qo(8:9)); if arm==1 ddt=0; end end % ReDrawing the Animation: if vr==1 || ml==1 drawnow; end % Starting a timer: tic ANG=zeros(1,n+1);

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Appendix B (continued) 99 while i<=(n+1) %Calculating the angle between the trajectory and the wheelchair's x axis the=WMRA_opt_angle(Td,Ti,Towc,L,T01, T12, T23, T34, T45, T56, T67); ANG(i)=the; % Starting the Iteration Loop: % Calculating the 6X7 Jacobian of the arm in frame 0: [Joa,detJoa]=WMRA_J07(T01, T12, T23, T34, T45, T56, T67); % Calculating the 6X2 Jacobian based on the WMRA's base in the ground frame: phi=atan2(Towc(2,1),Towc(1,1)); Jowc=WMRA_Jga(1, phi, Toa(1:2,4)); % Changing the Jacobian reference frame based on the choice of which coordinates frame are referenced in the Cartesian control: % coord=1 for Ground Coordinates Control. % coord=2 for Wheelchair Coordinates Control. % coord=3 for Gripper Coordinates Control. if coord==2 Joa=Joa; Jowc=[Towc(1:3,1:3)' zeros(3); zeros(3) Towc(1:3,1:3)']*Jowc; elseif coord==3 Joa=[Toa(1:3,1:3)' zeros(3); zeros(3) Toa(1:3,1:3)']*Joa; Jowc=[To(1:3,1:3)' zeros(3); zeros(3) To(1:3,1:3)']*Jowc; elseif coord==1 Joa=[Towc(1:3,1:3) zeros(3); zeros(3) Towc(1:3,1:3)]*Joa; Jowc=Jowc; end % Calculating the 3X9 or 6X9 augmented Jacobian of the WMRA system based on the ground frame: if cart==2 Joa=Joa(1:3,1:7); detJoa=sqrt(det(Joa*Joa')); Jowc=Jowc(1:3,1:2); Jo=[Joa Jowc]; detJo=sqrt(det(Jo*Jo')); else Jo=[Joa Jowc]; detJo=sqrt(det(Jo*Jo')); end % Finding the Cartesian errors of the end effector: if cont==1 || cont==6 % Calculating the Position and Orientation errors of the end effector, and the rates of motion of the end effector: if coord==2 invTowc=[Towc(1:3,1:3)' Towc(1:3,1:3)'*Towc(1:3,4);0 0 0 1];

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Appendix B (continued) 100 Ttnew=invTowc*Tiwc*Tt(:,:,i); dx=WMRA_delta(Toa, Ttnew); elseif coord==3 invTo=[To(1:3,1:3)' To(1:3,1:3)'*To(1:3,4);0 0 0 1]; Ttnew=invTo*Ti*Tt(:,:,i); dx=WMRA_delta(eye(4), Ttnew); else dx=WMRA_delta(To, Tt(:,:,i)); end elseif cont==2 elseif cont==3 dx=v*dt*[spdata1(3)/20 ; spdata1(1)/40 ; spdata1(2)/30 ; spdata1(6)/1500 ; spdata1(4)/900 ; spdata1(5)/1300]; dg=spdata1(7); elseif cont==4 dx=v*dt*WMRA_psy(port1); dg=dx(7); dx=dx(1:6); else dx=v*dt*VAR_DX(1:6); dg=VAR_DX(7); end % Changing the order of Cartesian motion in the case when gripper reference frame is selected for control with the screen or psy or SpaceBall interfaces: if coord==3 && cont>=3 dx=[dx(2);dx(3);dx(1);dx(5);dx(6);dx(4)]; end if cart==2 dx=dx(1:3); end % Calculating the resolved rate with optimization: % Index input values for "optim": 1= SRI & WLN, 2= PI & WLN, 3= SRI & ENE, 4= PI & ENE: if WCA==2 dq=WMRA_Opt(optim, JLA, JLO, Joa, detJoa, dq(1:7), dx, dt, qo,the,n,choice0); dq=[dq;0;0]; elseif WCA==3 dq=WMRA_Opt(optim, JLA, JLO, Jowc, 1, dq(8:9), dx(1:2), dt, 1,the,n,choice0); dq=[0;0;0;0;0;0;0;dq]; else dq=WMRA_Opt(optim, JLA, JLO, Jo, detJo, dq, dx, dt, qo,the,n,choice0); end % Calculating the new Joint Angles:

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Appendix B (continued) 101 qn=qo+dq; % Calculating the new Transformation Matrices: [Tn, Tna, Tnwc, T01, T12, T23, T34, T45, T56, T67]=WMRA_Tall(2, qn, dq(8:9), Towc); % A safety condition function to stop the joints that may cause colision of the arm with itself, the wheelchair, or the human user: if JLO==1 && WCA~=3 dq(1:7)=WMRA_collide(dq(1:7), T01, T12, T23, T34, T45, T56, T67); % Recalculating the new Joint Angles: qn=qo+dq; % Recalculating the new Transformation Matrices: [Tn, Tna, Tnwc, T01, T12, T23, T34, T45, T56, T67]=WMRA_Tall(2, qn, dq(8:9), Towc); end % Saving the plot data in case plots are required: if plt==2 WMRA_Plots(1, L, r2d, dt, i, tt, qn, dq, Tn, Tnwc, detJoa, detJo); end % Updating Physical Arm: if arm==1 ddt=ddt+dt; if ddt>=0.5 || i>=(n+1) WMRA_ARM_Motion(2, 1, [qn;dg], ddt); ddt=0; end end % Updating Virtual Reality Animation: if vr==1 WMRA_VR_Animation(2, Tnwc, qn); end % Updating Matlab Graphics Animation: if ml==1 WMRA_ML_Animation(2, Ti, Td, Tnwc, T01, T12, T23, T34, T45, T56, T67); end % ReDrawing the Animation: if vr==1 || ml==1 drawnow; end % Updating the old values with the new values for the next iteration: qo=qn;

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Appendix B (continued) 102 To=Tn; Toa=Tna; Towc=Tnwc; tt=tt+dt; i=i+1; % Stopping the simulation when the exit button is pressed: if cont==3 || cont==4 || cont==5 if (VAR_SCREENOPN == 1) n=n+1; else break end end % Delay to comply with the required speed: if toc < tt pause(tttoc); end end % Reading the elapsed time and printing it with the simulation time: if cont==1 || cont==2 || cont==6, fprintf(' \ nSimula. time is %6.6f seconds.\ n' total_time); end toc % Plotting: if vr==1 || ml==1 || arm==1 %Orienting the Wheelchair to a desired final orientation choice9 = input(' \ n Do you want to rotate the wheelchair? \ n Press "1" for Yes, or press "2" for No. \ n', 's'); if choice9=='1' ang = input(' \ n enter the desired angle in radians \ n'); WMRA_final_orientation(2, vr, ml, arm, Tnwc, qn,ang) else ang=0; end if plt==2 WMRA_Plots(2, L, r2d, dt, i, tt, qn, dq, Tn, Tnwc, detJoa, detJo); end % Going back to the ready position: %choice6 = input('\ n Do you want to go back to the "ready" position? \ n Press "1" for Yes, or press "2" for No. \ n','s'); choice6 ='2'; if choice6=='1' WMRA_any2ready(2, vr, ml, arm, Tnwc, qn); % Going back to the parking position: choice7 = input(' \ n Do you want to go back to the "parking" position? \ n Press "1" for Yes, or press "2" for No. \ n', 's');

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Appendix B (continued) 103 if choice7=='1' WMRA_ready2park(2, vr, ml, arm, Tnwc, qn(8:9)); end end % Closing the Arm library and Matlab Graphics Animation and Virtual Reality Animation and Plots windows: %choice8 = input('\ n Do you want to close all simulation windows and arm controls? \ n Press "1" for Yes, or press "2" for No. \ n','s'); choice8 ='2'; if choice8=='1' if arm==1 WMRA_ARM_Motion(3, 0, 0, 0); end if vr==1 WMRA_VR_Animation(3, 0, 0); end if ml==1 WMRA_ML_Animation(3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0); end if plt==2 close (figure(2),figure(3),figure(4),figure(5),figure(6),figure(7),figure(8), figure(9),figure(10),figure(12)); end end end qn=[qn(1:8);qn(9)+ang] Tnwc WMRA_Main_Open(qn,Tnwc) WMRA_Main_Open % This is a simplified version of the Main program to acomplish a subtask % with motion control. most of the options are prespecified and will not be % changed by the user % Declaring the global variables to be used for the touch screen control: function WMRA_Main_Open(qn,Tnwc) global VAR_DX global VAR_SCREENOPN global dHo % Defining used parameters:

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Appendix B (continued) 104 d2r=pi/180; % Conversions from Degrees to Radians. r2d=180/pi; % Conversions from Radians to Degrees. % Reading the Wheelchair's constant dimentions, all dimentions are converted in millimeters: L=WMRA_WCD; radi=1000; e=1; % User input prompts: %choice000 = input('\ n Choose what to control: \ n For combined Wheelchair and Arm control, press "1", \ n For Arm only control, press "2", \ n For Wheelchair only control, press "3". \ n','s'); choice000 = 1; WCA=1; %choice00000 = input('\ n Choose whose frame to base the control on: \ n For Ground Frame, press "1", \ n For Wheelchair Frame, press "2", \ n For Gripper Frame, press "3". \ n','s'); choice00000=1; coord=1; %choice0000 = input('\ n Choose the cartesian coordinates to be controlled: \ n For Position and Orientation, press "1", \ n For Position only, press "2". \ n','s'); choice0000 =1; cart=1; %choice5 = input('\ n Please enter the desired optimization method: (1= SRI & WLN, 2= PI & WLN, 3= SRI & ENE, 4= PI & ENE) \ n','s'); choice5 =1; optim=1; %choice50 = input('\ n Do you want to include Joint Limit Avoidance? (1= Yes, 2= No) \ n','s'); choice50 =1; JLA=1; %choice500 = input('\ n Do you want to include Joint Limit/Velocity and Obstacle Safety Stop? (1= Yes, 2= No) \ n','s'); choice500 = 1; JLO=1; %choice0 = input('\ n Choose the control mode: \ n For circle control, press "6", \ n For position control, press "1", \ n For velocity control, press "2", \ n For SpaceBall control, press "3", \ n For Psychology Mask control, press "4", \ n For Touch Screen control, press "5",\ n For Switch, press "7". \ n','s'); choice0 ='6'; if choice0=='1' cont=1; %Td = input('\ n Please enter the transformation matrix of the desired position and orientation from the controlbased frame \ n (e.g. [0 0 1 1455;1 0 0 369;0 1 0 999; 0 0 0 1]) \ n'); Td=[0 0 1 1955;1 0 0 1169;0 1 0 999; 0 0 0 1] *WMRA_rotx(pi/6)*WMRA_roty(pi/4); %v = input('\ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); v=50;

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Appendix B (continued) 105 %choice00 = input('\ n Chose the Trajectory generation function: \ n Press "1" for a Polynomial function with Blending, or \ n press "2" for a Polynomial function without Blending, or \ n press "3" for a Linear function.\ n','s'); choice00=1; trajf=1; elseif choice0=='7' cont=1; Td = [0 0 1 1455;1 0 0 369;0 1 0 999; 0 0 0 1]; v = input(' \ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); choice00 = input(' \ n Chose the Trajectory generation function: \ n Press "1" for a Polynomial function with Blending, or \ n press "2" for a Polynomial function without Blending, or \ n press "3" for a Linear function.\ n', 's'); if choice00=='2' trajf=2; elseif choice00=='3' trajf=3; else trajf=1; end elseif choice0=='2' cont=2; ts = input(' \ n Please enter the desired simulation time in seconds (e.g. 2) \ n'); if cart==2 Vd = input(' \ n Please enter the desired 3x1 cartesian velocity vector of the gripper (in mm/s) (e.g. [70;70;70]) \ n'); else Vd = input( \ n Please enter the desired 6x1 cartesian velocity vector of the gripper (in mm/s, radians/s) (e.g. [70;70;70;0.001;0.001;0.001]) \ n'); end elseif choice0=='3' cont=3; % Space Ball will be used for control. v = input(' \ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); elseif choice0=='4' cont=4; % BCI 2000 Psychology Mask will be used for control. v = input(' \ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); port1 = input(' \ n Please enter the desired port number (e.g. 19711) \ n'); choice00 = input(' \ n Chose the Trajectory generation function: \ n Press "1" for a Polynomial function with Blending, or \ n press "2" for a Polynomial function without Blending, or \ n press "3" for a Linear function, or \ n press "4" for a Circular Polynomial function with Blending. \ n', 's'); elseif choice0=='6' choice0=6;

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Appendix B (continued) 106 cont=6; %radi = input('\ n Please enter the radius of the cirle in mm (e.g. 1000) \ n'); radi=1000; %e = input('\ n If the door opens to the left press "1".\ n If it opens to the right press "2" \ n'); e=2; %v = input('\ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); v=50; trajf=4; else cont=5; % Touch Screen will be used for control. v = input(' \ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); end choice1 = input(' \ n Choose animation type or no animation: \ n For Virtual Reality Animation, press "1", \ n For Matlab Graphics Animation, press "2", \ n For BOTH Animations, press "3", \ n For NO Animation, press "4". \ n', 's'); if choice1=='2' vr = 0; ml = 1; elseif choice1=='3' vr = 1; ml = 1; elseif choice1=='4' vr = 0; ml = 0; else vr = 1; ml = 0; end %choice10 = input('\ n Would you like to run the actual WMRA? \ n For yes, press "1", \ n For no, press "2". \ n','s'); choice10='2'; if choice10=='1' arm=1; else arm=0; end %choice2 = input('\ n Press "1" if you want to start at the "ready" position, \ n or press "2" if you want to enter the initial joint angles. \ n','s'); choice2='2'; if choice2=='2' %qi = input('\ n Please enter the arms initial angles vector in radians (e.g. [pi/2;pi/2;0;pi/2;pi/2;pi/2;0]) \ n'); %WCi = input('\ n Please enter the initial x,y position and z orientation of the WMRA base from the ground base in millimeters and radians (e.g. [200;500;0.3]) \ n'); qi=qn(1:7); ini=0; else

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Appendix B (continued) 107 qi=[90;90;0;90;90;90;0]*d2r; WCi=[0;0;0]; ini=0; if vr==1 || ml==1 || arm==1 %choice3 = input('\ n Press "1" if you want to include "park" to "ready" motion, \ n or press "2" if not. \ n','s'); choice3= '1'; if choice3=='2' ini=0; else ini=1; end end end %choice4 = input('\ n Press "1" if you do NOT want to plot the simulation results, \ n or press "2" if do. \ n','s'); choice4 ='2'; if choice4=='2' plt=2; else plt=1; end % Calculating the Transformation Matrix of the initial position of the WMRA's base: Tiwc=Tnwc; % Calculating the initial Wheelchair Variables: qiwc=[qn(8);qn(9)]; % Calculating the initial transformation matrices: [Ti, Tia, Tiwc, T01, T12, T23, T34, T45, T56, T67]=WMRA_Tall(1, qi, [0;0], Tiwc); if cont==1 % Calculating the linear distance from the initial position to the desired position and the linear velocity: if coord==2 D=sqrt( (Td(1,4)Tia(1,4))^2 + (Td(2,4)Tia(2,4))^2 + (Td(3,4)Tia(3,4))^2); elseif coord==3 D=sqrt( (Td(1,4))^2 + (Td(2,4))^2 + (Td(3,4))^2); else D=sqrt( (Td(1,4)Ti(1,4))^2 + (Td(2,4)Ti(2,4))^2 + (Td(3,4)Ti(3,4))^2); end % Calculating the number of iteration and the time increment (delta t) if the linear step increment of the tip is 1 mm: dt=0.05; % Time increment in seconds. total_time=D/v; % Total time of animation. n=round(total_time/dt); % Number of iterations rounded up. dt=total_time/n; % Adjusted time increment in seconds.

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Appendix B (continued) 108 % Calculating the Trajectory of the end effector, and once the trajectory is calculated, we should redefine "Td" based on the ground frame: if coord==2 Tt=WMRA_traj(radi,trajf, Tia, Td, n+1); Td=Tiwc*Td; elseif coord==3 Tt=WMRA_traj(radi,trajf, eye(4), Td, n+1); Td=Ti*Td; else Tt=WMRA_traj(radi,trajf, Ti, Td, n+1); end elseif cont==2 % Calculating the number of iterations and the time increment (delta t) if the linear step increment of the gripper is 1 mm: dt=0.05; % Time increment in seconds. total_time=ts; % Total time of animation. n=round(total_time/dt); % Number of iterations rounded up. dt=total_time/n; % Adjusted time increment in seconds. dx=Vd*dt; Td=Ti; elseif cont==3 WMRA_exit(); % This is to stop the simulation in SpaceBall control when the user presses the exit key. dt=0.05; dx=v*dt*[spdata1(3)/20 ; spdata1(1)/40 ; spdata1(2)/30 ; spdata1(6)/1500 ; spdata1(4)/900 ; spdata1(5)/1300]; dg=spdata1(7); Td=Ti; n=1; elseif cont==4 WMRA_exit(); % This is to stop the simulation in Psychology Mask control when the user presses the exit key. dt=0.05; dx=v*dt*WMRA_psy(port1); dg=dx(7); dx=dx(1:6); Td=Ti; n=1; elseif cont==6 % Calculating the desired transformation matrix based on the radius: Tdoor=Ti; Tdoor(1,4)=Ti(1,4)+radi/2; Tdoor(2,4)=Ti(2,4)+radi/2; Td=Tdoor; Td(1,4)=Td(1,4)radi; Td(2,4)=Td(2,4)((1)^e)*radi; % Calculating the circular distance from the initial position to the desired position and the linear velocity: D=0.5*pi*radi; % Calculating the number of iteration and the time increment (delta t) if the linear step increment of the tip is 1 mm:

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Appendix B (continued) 109 dt=0.05; % Time increment in seconds. total_time=D/v; % Total time of animation. n=round(total_time/dt); % Number of iterations rounded up. dt=total_time/n; % Adjusted time increment in seconds. % Calculating the Trajectory of the end effector, and once the trajectory is calculated, we should redefine "Td" based on the ground frame: if coord==2 Tt=WMRA_traj(radi,trajf, Tia, Td, n+1,e); Td=Tiwc*Td; elseif coord==3 Tt=WMRA_traj(radi,trajf, eye(4), Td, n+1,e); Td=Ti*Td; else Tt=WMRA_traj(radi,trajf, Ti, Td, n+1,e); end else WMRA_screen('0'); % This is to start the screen controls. Argument: '0'=BACK button disabled, '1'=BACK button enabled. dt=0.05; dx=v*dt*VAR_DX(1:6); dg=VAR_DX(7); Td=Ti; n=1; end % Initializing the joint angles, the Transformation Matrix, and time: dq=zeros(9,1); dg=0; qo=[qi;qiwc]; To=Ti; Toa=Tia; Towc=Tiwc; tt=0; i=1; dHo=[0;0;0;0;0;0;0]; % Starting a timer: tic while i<=(n+1) %Calculating the angle between the trajectory and the wheelchair's x axis the=WMRA_opt_angle(Td,Ti,Towc,L,T01, T12, T23, T34, T45, T56, T67); % Starting the Iteration Loop: % Calculating the 6X7 Jacobian of the arm in frame 0: [Joa,detJoa]=WMRA_J07(T01, T12, T23, T34, T45, T56, T67);

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Appendix B (continued) 110 % Calculating the 6X2 Jacobian based on the WMRA's base in the ground frame: phi=atan2(Towc(2,1),Towc(1,1)); Jowc=WMRA_Jga(1, phi, Toa(1:2,4)); % Changing the Jacobian reference frame based on the choice of which coordinates frame are referenced in the Cartesian control: % coord=1 for Ground Coordinates Control. % coord=2 for Wheelchair Coordinates Control. % coord=3 for Gripper Coordinates Control. if coord==2 Joa=Joa; Jowc=[Towc(1:3,1:3)' zeros(3); zeros(3) Towc(1:3,1:3)']*Jowc; elseif coord==3 Joa=[Toa(1:3,1:3)' zeros(3); zeros(3) Toa(1:3,1:3)']*Joa; Jowc=[To(1:3,1:3)' zeros(3); zeros(3) To(1:3,1:3)']*Jowc; elseif coord==1 Joa=[Towc(1:3,1:3) zeros(3); zeros(3) Towc(1:3,1:3)]*Joa; Jowc=Jowc; end % Calculating the 3X9 or 6X9 augmented Jacobian of the WMRA system based on the ground frame: if cart==2 Joa=Joa(1:3,1:7); detJoa=sqrt(det(Joa*Joa')); Jowc=Jowc(1:3,1:2); Jo=[Joa Jowc]; detJo=sqrt(det(Jo*Jo')); else Jo=[Joa Jowc]; detJo=sqrt(det(Jo*Jo')); end % Finding the Cartesian errors of the end effector: if cont==1 || cont==6 % Calculating the Position and Orientation errors of the end effector, and the rates of motion of the end effector: if coord==2 invTowc=[Towc(1:3,1:3)' Towc(1:3,1:3)'*Towc(1:3,4);0 0 0 1]; Ttnew=invTowc*Tiwc*Tt(:,:,i); dx=WMRA_delta(Toa, Ttnew); elseif coord==3 invTo=[To(1:3,1:3)' To(1:3,1:3)'*To(1:3,4);0 0 0 1]; Ttnew=invTo*Ti*Tt(:,:,i); dx=WMRA_delta(eye(4), Ttnew); else dx=WMRA_delta(To, Tt(:,:,i)); end elseif cont==2

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Appendix B (continued) 111 elseif cont==3 dx=v*dt*[spdata1(3)/20 ; spdata1(1)/40 ; spdata1(2)/30 ; spdata1(6)/1500 ; spdata1(4)/900 ; spdata1(5)/1300]; dg=spdata1(7); elseif cont==4 dx=v*dt*WMRA_psy(port1); dg=dx(7); dx=dx(1:6); else dx=v*dt*VAR_DX(1:6); dg=VAR_DX(7); end % Changing the order of Cartesian motion in the case when gripper reference frame is selected for control with the screen or psy or SpaceBall interfaces: if coord==3 && cont>=3 dx=[dx(2);dx(3);dx(1);dx(5);dx(6);dx(4)]; end if cart==2 dx=dx(1:3); end % Calculating the resolved rate with optimization: % Index input values for "optim": 1= SRI & WLN, 2= PI & WLN, 3= SRI & ENE, 4= PI & ENE: if WCA==2 dq=WMRA_Opt(optim, JLA, JLO, Joa, detJoa, dq(1:7), dx, dt, qo,the,n,choice0); dq=[dq;0;0]; elseif WCA==3 dq=WMRA_Opt(optim, JLA, JLO, Jowc, 1, dq(8:9), dx(1:2), dt, 1,the,n,choice0); dq=[0;0;0;0;0;0;0;dq]; else dq=WMRA_Opt(optim, JLA, JLO, Jo, detJo, dq, dx, dt, qo,the,n,choice0); end % Calculating the new Joint Angles: qn=qo+dq; % Calculating the new Transformation Matrices: [Tn, Tna, Tnwc, T01, T12, T23, T34, T45, T56, T67]=WMRA_Tall(2, qn, dq(8:9), Towc); % A safety condition function to stop the joints that may cause colision of the arm with itself, the wheelchair, or the human user: if JLO==1 && WCA~=3 dq(1:7)=WMRA_collide(dq(1:7), T01, T12, T23, T34, T45, T56, T67);

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Appendix B (continued) 112 % Recalculating the new Joint Angles: qn=qo+dq; % Recalculating the new Transformation Matrices: [Tn, Tna, Tnwc, T01, T12, T23, T34, T45, T56, T67]=WMRA_Tall(2, qn, dq(8:9), Towc); end % Saving the plot data in case plots are required: if plt==2 WMRA_Plots(1, L, r2d, dt, i, tt, qn, dq, Tn, Tnwc, detJoa, detJo); end % Updating Physical Arm: if arm==1 ddt=ddt+dt; if ddt>=0.5 || i>=(n+1) WMRA_ARM_Motion(2, 1, [qn;dg], ddt); ddt=0; end end % Updating Virtual Reality Animation: if vr==1 WMRA_VR_Animation(2, Tnwc, qn); end % Updating Matlab Graphics Animation: if ml==1 WMRA_ML_Animation(2, Ti, Td, Tnwc, T01, T12, T23, T34, T45, T56, T67); end % ReDrawing the Animation: if vr==1 || ml==1 drawnow; end % Updating the old values with the new values for the next iteration: qo=qn; To=Tn; Toa=Tna; Towc=Tnwc; tt=tt+dt; i=i+1; % Stopping the simulation when the exit button is pressed: if cont==3 || cont==4 || cont==5 if (VAR_SCREENOPN == 1) n=n+1; else

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Appendix B (continued) 113 break end end % Delay to comply with the required speed: if toc < tt pause(tttoc); end end % Reading the elapsed time and printing it with the simulation time: if cont==1 || cont==2 || cont==6, fprintf(' \ nSimula. time is %6.6f seconds.\ n' total_time); end toc % Plotting: if plt==2 WMRA_Plots(2, L, r2d, dt, i, tt, qn, dq, Tn, Tnwc, detJoa, detJo); end if vr==1 || ml==1 || arm==1 %Orienting the Wheelchair to a desired final orientation choice9 = input(' \ n Do you want to rotate the wheelchair? \ n Press "1" for Yes, or press "2" for No. \ n', 's'); if choice9=='1' ang = input(' \ n enter the desired angle in radians \ n'); WMRA_final_orientation(2, vr, ml, arm, Tnwc, qn,ang) end % Going back to the ready position: %choice6 = input('\ n Do you want to go back to the "ready" position? \ n Press "1" for Yes, or press "2" for No. \ n','s'); choice6 ='2'; if choice6=='1' WMRA_any2ready(2, vr, ml, arm, Tnwc, qn); % Going back to the parking position: choice7 = input(' \ n Do you want to go back to the "parking" position? \ n Press "1" for Yes, or press "2" for No. \ n', 's'); if choice7=='1' WMRA_ready2park(2, vr, ml, arm, Tnwc, qn(8:9)); end end % Closing the Arm library and Matlab Graphics Animation and Virtual Reality Animation and Plots windows: %choice8 = input('\ n Do you want to close all simulation windows and arm controls? \ n Press "1" for Yes, or press "2" for No. \ n','s'); choice8 ='2'; if choice8=='1' if arm==1 WMRA_ARM_Motion(3, 0, 0, 0); end if vr==1

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Appendix B (continued) 114 WMRA_VR_Animation(3, 0, 0); end if ml==1 WMRA_ML_Animation(3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0); end if plt==2 close (figure(2),figure(3),figure(4),figure(5),figure(6),figure(7),figure(8), figure(9),figure(10),figure(12)); end end end end WMRA_Main_Reach % This is a simplified version of the Main program to acomplish a subtask % with motion control. most of the options are prespecified and will not be % changed by the user % Declaring the global variables to be used for the touch screen control: function WMRA_Main_Reach global VAR_DX global VAR_SCREENOPN global dHo % Defining used parameters: d2r=pi/180; % Conversions from Degrees to Radians. r2d=180/pi; % Conversions from Radians to Degrees. % Reading the Wheelchair's constant dimentions, all dimentions are converted in millimeters: L=WMRA_WCD; radi=1000; e=1; % User input prompts: %choice000 = input('\ n Choose what to control: \ n For combined Wheelchair and Arm control, press "1", \ n For Arm only control, press "2", \ n For Wheelchair only control, press "3". \ n','s'); choice000 = 1; WCA=1;

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Appendix B (continued) 115 %choice00000 = input('\ n Choose whose frame to base the control on: \ n For Ground Frame, press "1", \ n For Wheelchair Frame, press "2", \ n For Gripper Frame, press "3". \ n','s'); choice00000=1; coord=1; %choice0000 = input('\ n Choose the cartesian coordinates to be controlled: \ n For Position and Orientation, press "1", \ n For Position only, press "2". \ n','s'); choice0000 =1; cart=1; %choice5 = input('\ n Please enter the desired optimization method: (1= SRI & WLN, 2= PI & WLN, 3= SRI & ENE, 4= PI & ENE) \ n','s'); choice5 =1; optim=1; %choice50 = input('\ n Do you want to include Joint Limit Avoidance? (1= Yes, 2= No) \ n','s'); choice50 =1; JLA=1; %choice500 = input('\ n Do you want to include Joint Limit/Velocity and Obstacle Safety Stop? (1= Yes, 2= No) \ n','s'); choice500 = 1; JLO=1; %choice0 = input('\ n Choose the control mode: \ n For circle control, press "6", \ n For position control, press "1", \ n For velocity control, press "2", \ n For SpaceBall control, press "3", \ n For Psychology Mask control, press "4", \ n For Touch Screen control, press "5",\ n For Switch, press "7". \ n','s'); choice0 ='1'; if choice0=='1' cont=1; %Td = input('\ n Please enter the transformation matrix of the desired position and orientation from the controlbased frame \ n (e.g. [0 0 1 1455;1 0 0 369;0 1 0 999; 0 0 0 1]) \ n'); Td = [0 0 1 1455;1 0 0 1169;0 1 0 999; 0 0 0 1]; %v = input('\ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); v=50; %choice00 = input('\ n Chose the Trajectory generation function: \ n Press "1" for a Polynomial function with Blending, or \ n press "2" for a Polynomial function without Blending, or \ n press "3" for a Linear function.\ n','s'); choice00=1; trajf=1; elseif choice0=='7' cont=1; Td = [0 0 1 1455;1 0 0 369;0 1 0 999; 0 0 0 1]; v = input(' \ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); choice00 = input(' \ n Chose the Trajectory generation function: \ n Press "1" for a Polynomial function with Blending, or \ n press "2" for a Polynomial function without Blending, or \ n press "3" for a Linear function.\ n', 's'); if choice00=='2'

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Appendix B (continued) 116 trajf=2; elseif choice00=='3' trajf=3; else trajf=1; end elseif choice0=='2' cont=2; ts = input(' \ n Please enter the desired simulation time in seconds (e.g. 2) \ n'); if cart==2 Vd = input(' \ n Please enter the desired 3x1 cartesian velocity vector of the gripper (in mm/s) (e.g. [70;70;70]) \ n'); else Vd = input(' \ n Please enter the desired 6x1 cartesian velocity vector of the gripper (in mm/s, radians/s) (e.g. [70;70;70;0.001;0.001;0.001]) \ n'); end elseif choice0=='3' cont=3; % Space Ball will be used for control. v = input(' \ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); elseif choice0=='4' cont=4; % BCI 2000 Psychology Mask will be used for control. v = input(' \ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); port1 = input(' \ n Please enter the desired port number (e.g. 19711) \ n'); choice00 = input(' \ n Chose the Trajectory generation function: \ n Press "1" for a Polynomial function with Blending, or \ n press "2" for a Polynomial function without Blending, or \ n press "3" for a Linear function, or \ n press "4" for a Circular Polynomial function with Blending. \ n', 's'); elseif choice0=='6' choice0=6; cont=6; %radi = input('\ n Please enter the radius of the cirle in mm (e.g. 1000) \ n'); radi=1000; %e = input('\ n If the door opens to the left press "1".\ n If it opens to the right press "2" \ n'); e=2; %v = input('\ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n'); v=50; trajf=4; else cont=5; % Touch Screen will be used for control. v = input(' \ n Please enter the desired linear velocity of the gripper in mm/s (e.g. 50) \ n');

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Appendix B (continued) 117 end choice1 = input(' \ n Choose animation type or no animation: \ n For Virtual Reality Animation, press "1", \ n For Matlab Graphics Animation, press "2", \ n For BOTH Animations, press "3", \ n For NO Animation, press "4". \ n', 's'); if choice1=='2' vr = 0; ml = 1; elseif choice1=='3' vr = 1; ml = 1; elseif choice1=='4' vr = 0; ml = 0; else vr = 1; ml = 0; end %choice10 = input('\ n Would you like to run the actual WMRA? \ n For yes, press "1", \ n For no, press "2". \ n','s'); choice10='2'; if choice10=='1' arm=1; else arm=0; end %choice2 = input('\ n Press "1" if you want to start at the "ready" position, \ n or press "2" if you want to enter the initial joint a ngles. \ n','s'); choice2='1'; if choice2=='2' qi = input(' \ n Please enter the arms initial angles vector in radians (e.g. [pi/2;pi/2;0;pi/2;pi/2;pi/2;0]) \ n'); WCi = input(' \ n Please enter the initial x,y position and z orientation of the WMRA base from the ground base in millimeters and radians (e.g. [200;500;0.3]) \ n'); ini=0; else qi=[90;90;0;90;90;90;0]*d2r; WCi=[0;0;0]; ini=0; if vr==1 || ml==1 || arm==1 %choice3 = input('\ n Press "1" if you want to include "park" to "ready" motion, \ n or press "2" if not. \ n','s'); choice3= '1'; if choice3=='2' ini=0; else ini=1; end end end %choice4 = input('\ n Press "1" if you do NOT want to plot the simulation results, \ n or press "2" if do. \ n','s'); choice4 ='2';

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Appendix B (continued) 118 if choice4=='2' plt=2; else plt=1; end % Calculating the Transformation Matrix of the initial position of the WMRA's base: Tiwc=WMRA_p2T(WCi(1),WCi(2),WCi(3)); % Calculating the initial Wheelchair Variables: qiwc=[sqrt(WCi(1)^2+WCi(2)^2);WCi(3)]; % Calculating the initial transformation matrices: [Ti, Tia, Tiwc, T01, T12, T23, T34, T45, T56, T67]=WMRA_Tall(1, qi, [0;0], Tiwc); if cont==1 % Calculating the linear distance from the initial position to the desired position and the linear velocity: if coord==2 D=sqrt( (Td(1,4)Tia(1,4))^2 + (Td(2,4)Tia(2,4))^2 + (Td(3,4)Tia(3,4))^2); elseif coord==3 D=sqrt( (Td(1,4))^2 + (Td(2,4))^2 + (Td(3,4))^2); else D=sqrt( (Td(1,4)Ti(1,4))^2 + (Td(2,4)Ti(2,4))^2 + (Td(3,4)Ti(3,4))^2); end % Calculating the number of iteration and the time increment (delta t) if the linear step increment of the tip is 1 mm: dt=0.05; % Time increment in seconds. total_time=D/v; % Total time of animation. n=round(total_time/dt); % Number of iterations rounded up. dt=total_time/n; % Adjusted time increment in seconds. % Calculating the Trajectory of the end effector, and once the trajectory is calculated, we should redefine "Td" based on the ground frame: if coord==2 Tt=WMRA_traj(radi,trajf, Tia, Td, n+1); Td=Tiwc*Td; elseif coord==3 Tt=WMRA_traj(radi,trajf, eye(4), Td, n+1); Td=Ti*Td; else Tt=WMRA_traj(radi,trajf, Ti, Td, n+1); end elseif cont==2 % Calculating the number of iterations and the time increment (delta t) if the linear step increment of the gripper is 1 mm: dt=0.05; % Time increment in seconds. total_time=ts; % Total time of animation.

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Appendix B (continued) 119 n=round(total_time/dt); % Number of iterations rounded up. dt=total_time/n; % Adjusted time increment in seconds. dx=Vd*dt; Td=Ti; elseif cont==3 WMRA_exit(); % This is to stop the simulation in SpaceBall control when the user presses the exit key. dt=0.05; dx=v*dt*[spdata1(3)/20 ; spdata1(1)/40 ; spdata1(2)/30 ; spdata1(6)/1500 ; spdata1(4)/900 ; spdata1(5)/1300]; dg=spdata1(7); Td=Ti; n=1; elseif cont==4 WMRA_exit(); % This is to stop the simulation in Psychology Mask control when the user presses the exit key. dt=0.05; dx=v*dt*WMRA_psy(port1); dg=dx(7); dx=dx(1:6); Td=Ti; n=1; elseif cont==6 % Calculating the desired transformation matrix based on the radius: Tdoor=Ti; Tdoor(1,4)=Ti(1,4)+radi/2; Tdoor(2,4)=Ti(2,4)+radi/2; Td=Tdoor; Td(1,4)=Td(1,4)radi; Td(2,4)=Td(2,4)((1)^e)*radi; % Calculating the circular distance from the initial position to the desired position and the linear velocity: D=0.5*pi*radi; % Calculating the number of iteration and the time increment (delta t) if the linear step increment of the tip is 1 mm: dt=0.05; % Time increment in seconds. total_time=D/v; % Total time of animation. n=round(total_time/dt); % Number of iterations rounded up. dt=total_time/n; % Adjusted time increment in seconds. % Calculating the Trajectory of the end effector, and once the trajectory is calculated, we should redefine "Td" based on the ground frame: if coord==2 Tt=WMRA_traj(radi,trajf, Tia, Td, n+1,e); Td=Tiwc*Td; elseif coord==3 Tt=WMRA_traj(radi,trajf, eye(4), Td, n+1,e); Td=Ti*Td; else Tt=WMRA_traj(radi,trajf, Ti, Td, n+1,e); end else

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Appendix B (continued) 120 WMRA_screen('0'); % This is to start the screen controls. Argument: '0'=BACK button disabled, '1'=BACK button enabled. dt=0.05; dx=v*dt*VAR_DX(1:6); dg=VAR_DX(7); Td=Ti; n=1; end % Initializing the joint angles, the Transformation Matrix, and time: dq=zeros(9,1); dg=0; qo=[qi;qiwc]; To=Ti; Toa=Tia; Towc=Tiwc; tt=0; i=1; dHo=[0;0;0;0;0;0;0]; % Initializing the WMRA: if ini==0 % When no "park" to "ready" motion required. % Initializing Virtual Reality Animation: if vr==1 WMRA_VR_Animation(1, Towc, qo); end % Initializing Robot Animation in Matlab Graphics: if ml==1 WMRA_ML_Animation(1, To, Td, Towc, T01, T12, T23, T34, T45, T56, T67); end % Initializing the Physical Arm: if arm==1 WMRA_ARM_Motion(1, 2, [qo;dg], 0); ddt=0; end elseif ini==1 && (vr==1 || ml==1 || arm==1) % When "park" to "ready" motion is required. WMRA_park2ready(1, vr, ml, arm, Towc, qo(8:9)); if arm==1 ddt=0; end end % ReDrawing the Animation: if vr==1 || ml==1 drawnow; end % Starting a timer: tic ANG=zeros(1,n+1);

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Appendix B (continued) 121 bmax=WMRA_opt_angle(Td,Ti,Towc,L,T01, T12, T23, T34, T45, T56, T67); while i<=(n+1) %Calculating the angle between the trajectory and the wheelchair's x axis the=WMRA_opt_angle(Td,Ti,Towc,L,T01, T12, T23, T34, T45, T56, T67); ANG(i)=the; % Starting the Iteration Loop: % Calculating the 6X7 Jacobian of the arm in frame 0: [Joa,detJoa]=WMRA_J07(T01, T12, T23, T34, T45, T56, T67); % Calculating the 6X2 Jacobian based on the WMRA's base in the ground frame: phi=atan2(Towc(2,1),Towc(1,1)); Jowc=WMRA_Jga(1, phi, Toa(1:2,4)); % Changing the Jacobian reference frame based on the choice of which coordinates frame are referenced in the Cartesian control: % coord=1 for Ground Coordinates Control. % coord=2 for Wheelchair Coordinates Control. % coord=3 for Gripper Coordinates Control. if coord==2 Joa=Joa; Jowc=[Towc(1:3,1:3)' zeros(3); zeros(3) Towc(1:3,1:3)']*Jowc; elseif coord==3 Joa=[Toa(1:3,1:3)' zeros(3); zeros(3) Toa(1:3,1:3)']*Joa; Jowc=[To(1:3,1:3)' zeros(3); zeros(3) To(1:3,1:3)']*Jowc; elseif coord==1 Joa=[Towc(1:3,1:3) zeros(3); zeros(3) Towc(1:3,1:3)]*Joa; Jowc=Jowc; end % Calculating the 3X9 or 6X9 augmented Jacobian of the WMRA system based on the ground frame: if cart==2 Joa=Joa(1:3,1:7); detJoa=sqrt(det(Joa*Joa')); Jowc=Jowc(1:3,1:2); Jo=[Joa Jowc]; detJo=sqrt(det(Jo*Jo')); else Jo=[Joa Jowc]; detJo=sqrt(det(Jo*Jo')); end % Finding the Cartesian errors of the end effector: if cont==1 || cont==6 % Calculating the Position and Orientation errors of the end effector, and the rates of motion of the end effector: if coord==2

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Appendix B (continued) 122 invTowc=[Towc(1:3,1:3)' Towc(1:3,1:3)'*Towc(1:3,4);0 0 0 1]; Ttnew=invTowc*Tiwc*Tt(:,:,i); dx=WMRA_delta(Toa, Ttnew); elseif coord==3 invTo=[To(1:3,1:3)' To(1:3,1:3)'*To(1:3,4);0 0 0 1]; Ttnew=invTo*Ti*Tt(:,:,i); dx=WMRA_delta(eye(4), Ttnew); else dx=WMRA_delta(To, Tt(:,:,i)); end elseif cont==2 elseif cont==3 dx=v*dt*[spdata1(3)/20 ; spdata1(1)/40 ; spdata1(2)/30 ; spdata1(6)/1500 ; spdata1(4)/900 ; spdata1(5)/1300]; dg=spdata1(7); elseif cont==4 dx=v*dt*WMRA_psy(port1); dg=dx(7); dx=dx(1:6); else dx=v*dt*VAR_DX(1:6); dg=VAR_DX(7); end % Changing the order of Cartesian motion in the case when gripper reference frame is selected for control with the screen or psy or SpaceBall interfaces: if coord==3 && cont>=3 dx=[dx(2);dx(3);dx(1);dx(5);dx(6);dx(4)]; end if cart==2 dx=dx(1:3); end % Calculating the resolved rate with optimization: % Index input values for "optim": 1= SRI & WLN, 2= PI & WLN, 3= SRI & ENE, 4= PI & ENE: if WCA==2 dq=WMRA_Opt(optim, JLA, JLO, Joa, detJoa, dq(1:7), dx, dt, qo,the,n,choice0,bmax); dq=[dq;0;0]; elseif WCA==3 dq=WMRA_Opt(optim, JLA, JLO, Jowc, 1, dq(8:9), dx(1:2), dt, 1,the,n,choice0,bmax); dq=[0;0;0;0;0;0;0;dq]; else dq=WMRA_Opt(optim, JLA, JLO, Jo, detJo, dq, dx, dt, qo,the,n,choice0,bmax); end

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Appendix B (continued) 123 % Calculating the new Joint Angles: qn=qo+dq; % Calculating the new Transformation Matrices: [Tn, Tna, Tnwc, T01, T12, T23, T34, T45, T56, T67]=WMRA_Tall(2, qn, dq(8:9), Towc); % A safety condition function to stop the joints that may cause colision of the arm with itself, the wheelchair, or the human user: if JLO==1 && WCA~=3 dq(1:7)=WMRA_collide(dq(1:7), T01, T12, T23, T34, T45, T56, T67); % Recalculating the new Joint Angles: qn=qo+dq; % Recalculating the new Transformation Matrices: [Tn, Tna, Tnwc, T01, T12, T23, T34, T45, T56, T67]=WMRA_Tall(2, qn, dq(8:9), Towc); end % Saving the plot data in case plots are required: if plt==2 WMRA_Plots(1, L, r2d, dt, i, tt, qn, dq, Tn, Tnwc, detJoa, detJo); end % Updating Physical Arm: if arm==1 ddt=ddt+dt; if ddt>=0.5 || i>=(n+1) WMRA_ARM_Motion(2, 1, [qn;dg], ddt); ddt=0; end end % Updating Virtual Reality Animation: if vr==1 WMRA_VR_Animation(2, Tnwc, qn); end % Updating Matlab Graphics Animation: if ml==1 WMRA_ML_Animation(2, Ti, Td, Tnwc, T01, T12, T23, T34, T45, T56, T67); end % ReDrawing the Animation: if vr==1 || ml==1 drawnow; end

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Appendix B (continued) 124 % Updating the old values with the new values for the next iteration: qo=qn; To=Tn; Toa=Tna; Towc=Tnwc; tt=tt+dt; i=i+1; % Stopping the simulation when the exit button is pressed: if cont==3 || cont==4 || cont==5 if (VAR_SCREENOPN == 1) n=n+1; else break end end % Delay to comply with the required speed: if toc < tt pause(tttoc); end end % Reading the elapsed time and printing it with the simulation time: if cont==1 || cont==2 || cont==6, fprintf(' \ nSimula. time is %6.6f seconds.\ n' total_time); end toc % Plotting: if vr==1 || ml==1 || arm==1 %Orienting the Wheelchair to a desired final orientation choice9 = input(' \ n Do you want to rotate the wheelchair? \ n Press "1" for Yes, or press "2" for No. \ n', 's'); if choice9=='1' ang = input(' \ n enter the desired angle in radians \ n'); WMRA_final_orientation(2, vr, ml, arm, Tnwc, qn,ang) end if plt==2 WMRA_Plots(2, L, r2d, dt, i, tt, qn, dq, Tn, Tnwc, detJoa, detJo); end % Going back to the ready position: %choice6 = input('\ n Do you want to go back to the "ready" position? \ n Press "1" for Yes, or press "2" for No. \ n','s'); choice6 ='2'; if choice6=='1' WMRA_any2ready(2, vr, ml, arm, Tnwc, qn); % Going back to the parking position:

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Appendix B (continued) 125 choice7 = input(' \ n Do you want to go back to the "parking" position? \ n Press "1" for Yes, or press "2" for No. \ n', 's'); if choice7=='1' WMRA_ready2park(2, vr, ml, arm, Tnwc, qn(8:9)); end end % Closing the Arm library and Matlab Graphics Animation and Virtual Reality Animation and Plots windows: %choice8 = input('\ n Do you want to close all simulation windows and arm controls? \ n Press "1" for Yes, or press "2" for No. \ n','s'); choice8 ='2'; if choice8=='1' if arm==1 WMRA_ARM_Motion(3, 0, 0, 0); end if vr==1 WMRA_VR_Animation(3, 0, 0); end if ml==1 WMRA_ML_Animation(3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0); end if plt==2 close (figure(2),figure(3),figure(4),figure(5),figure(6),figure(7),figure(8), figure(9),figure(10),figure(12)); end end end TIME=[1:n+1]; Or=ANG+0.75; figure(17) plot(TIME,ANG,'LineWidth',5) axis([0 700 0 5]) grid on; title('Angle \ Theta Vs Iteration number');xlabel('Iteration number');ylabel(' \ Theta'); figure(15) plot(TIME,Or,'LineWidth',5) axis([0 700 0 5]) grid on; title('Wheechair orientation Vs Iteration number');xlabel('Iteration number');ylabel(' \ Orientation'); end

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Appendix B (continued) 126 WMRA_OP %###################################################################### #### % This M file creates optimized parameters for the weighted matrix values % of the wheels to account for positition during the % execution of a given trajectory. % Function Declaration function W1=WMRA_OP(the,i,n,bmax) if atan2(sin(the),cos(the))<0.3 W1=1; elseif atan2(sin(the),cos(the))~=0 W1=10; end WMRA_Opt % This function is for the resolved rate and optimization solution of the USF WMRA with 9 DOF. % Function Declaration: function [dq]=WMRA_Opt(i, JLA, JLO, Jo, detJo, dq, dx, dt, q,the,n,choice0,bmax) % Declaring a global variable: global dHo % Reading the Wheelchair's constant dimentions, all dimentions are converted in millimeters: L=WMRA_WCD; % The case when wheelchaironly control is required with no arm motion: if i==0 WCA=3; % claculating the Inverse of the Jacobian, which is always nonsingular: pinvJo=inv(Jo(1:2,1:2)); % calculating the joint angle change: % Here, dq of the wheels are translated from radians to distances travelled after using the Jacobian. dq=pinvJo*dx; dq(1)=dq(1)*L(5); else % Reading the physical joint limits of the arm: [qmin,qmax]=WMRA_Jlimit;

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Appendix B (continued) 127 % Creating the gradient of the optimization function to avoid joint limits: dH=[0;0;0;0;0;0;0]; if JLA==1 for j=1:7 dH(j)=0.25*(qmax(j)qmin(j))^2*(2*q(j)qmax(j)qmin(j))/((qmax(j)q(j))^2*(q(j)qmin(j))^2); % Redefining the weight in case the joint is moving away from it's limit or the joint limit was exceeded: if abs(dH(j)) < abs(dHo(j)) && q(j) < qmax(j) && q(j) > qmin(j) dH(j)=0; elseif abs(dH(j)) < abs(dHo(j)) && (q(j) >= qmax(j) || q(j) <= qmin(j)) dH(j)=inf; elseif abs(dH(j)) > abs(dHo(j)) && (q(j) >= qmax(j) || q(j) <= qmin(j)) dH(j)=0; end end end dHo=dH; % The case when armonly control is required with no wheelchair motion: if max(size(dq))==7 WCA=2; wo=20000000; ko=350000; % The weight matrix to be used for the Weighted Least Norm Solution with Joint Limit Avoidance: W=diag(1*[1;1;1;1;1;1;1]+1*abs(dH)); % The inverse of the diagonal weight matrix: dia=diag(W); Winv=diag([1/dia(1); 1/dia(2); 1/dia(3); 1/dia(4); 1/dia(5); 1/dia(6); 1/dia(7)]); % The case when wheelchairandarm control is required: else WCA=1; wo=34000000; ko=13; % The weight matrix to be used for the Weighted Least Norm Solution: if choice0==6; W=diag([1*[1;1;1;1;1;1;1]+1*abs(dH);0.5;1000]); else W=diag([1*[1;1;1;1;1;1;1]+1*abs(dH);WMRA_OP(the,i,n,bmax);WMRA_OR(the,i ,n,bmax)]); end % The inverse of the diagonal weight matrix: dia=diag(W); Winv=diag([1/dia(1); 1/dia(2); 1/dia(3); 1/dia(4); 1/dia(5); 1/dia(6); 1/dia(7); 1/dia(8); 1/dia(9)]); end

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Appendix B (continued) 128 % Redefining the determinant based on the weight: if i==1 || i==2 detJo=sqrt(det(Jo*Winv*Jo')); end dof=max(size(dx)); end % SRInverse and Weighted Least Norm Optimization: if i==1 % Calculating the variable scale factor, sf: if detJo
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Appendix B (continued) 129 end % claculating the SRInverse of the Jacobian: pinvJo=Jo'*inv(Jo*Jo'+sf*eye(dof)); % calculating the joint angle change optimized based on minimizing the Euclidean norm of errors: % Here, dq of the wheels are translated from distances travelled to radians, and back after using the Jacobian. if WCA==2 %dq=pinvJo*dx+(eye(7)pinvJo*Jo)*dq; dq=pinvJo*dx+0.001*(eye(7)pinvJo*Jo)*dH; else %dq(8)=dq(8)/L(5); %dq=pinvJo*dx+(eye(9)pinvJo*Jo)*dq; dq=pinvJo*dx+0.001*(eye(9)pinvJo*Jo)*[dH;0;0]; dq(8)=dq(8)*L(5); end % Pseudo Inverse and Projection Gradient Optimization based on Euclidean norm of errors: elseif i==4 % claculating the Pseudo Inverse of the Jacobian: pinvJo=Jo'*inv(Jo*Jo'); % calculating the joint angle change optimized based on minimizing the Euclidean norm of errors: % Here, dq of the wheels are translated from distances travelled to radians, and back after using the Jacobian. if WCA==2 %dq=pinvJo*dx+(eye(7)pinvJo*Jo)*dq; dq=pinvJo*dx+0.001*(eye(7)pinvJo*Jo)*dH; else %dq(8)=dq(8)/L(5); %dq=pinvJo*dx+(eye(9)pinvJo*Jo)*dq; dq=pinvJo*dx+0.001*(eye(9)pinvJo*Jo)*[dH;0;0]; dq(8)=dq(8)*L(5); end end if JLO==1 % A safety condition to stop the joint that reaches the joint limits in the arm: if WCA~=3 for k=1:7 if q(k) >= qmax(k) || q(k) <= qmin(k) dq(k)=0; end end end % A safety condition to slow the joint that exceeds the velocity limits in the WMRA: if WCA==3 dqmax=dt*[100;0.15]; % Joiny velocity limits when the time increment is dt second. else

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Appendix B (continued) 130 dqmax=dt*[0.5;0.5;0.5;0.5;0.5;0.5;0.5;100;0.15]; % Joiny velocity limits when the time increment is dt second. end for k=1:max(size(dq)) if abs(dq(k)) >= dqmax(k) dq(k)=sign(dq(k))*dqmax(k); end end end WMRA_opt_angle %###################################################################### #### %This MFile keeps track of the angel created between the projection of the %trajectory in the XY plane and the center axis of the whhechair. function the=WMRA_opt_angle(Td,Ti,Towc,L,T01, T12, T23, T34, T45, T56, T67) % Arm: T1=Towc*T01; T2=T1*T12; T3=T2*T23; T4=T3*T34; T5=T4*T45; T6=T5*T56; T7=T6*T67; Lt=sqrt((T7(1,4)Td(1,4))^2+(T7(2,4)Td(2,4))^2+(T7(3,4)Td(3,4))^2); %Updating the transformation matrices T8=Towc; % Arm Base Position. T9=T8*WMRA_transl(L(2),L(3),L(4)); % Wheelbase Center. T10=T9*WMRA_transl(0,L(1)/2,0); % Right Wheel Center. T11=T9*WMRA_transl(0,L(1)/2,0); % Left Wheel Center. V3D=[Td(1,4)Ti(1,4);Td(2,4)Ti(2,4);Td(3,4)Ti(3,4)]; %Let n be the normal vector to the plane Z = 0 n=[0;0;1]; %Computing the cross product between these two vectors will give us a %pivotal vector in the X Y plane: Vpiv=cross(V3D,n);

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Appendix B (continued) 131 %Then computing the cross product between this vector and the plane normal %again will result in the third vector of an orthogonal triad which is the %projection of the trajectory in the X Y plane: Vp=cross(n,Vpiv); %find the vector defined by the wheels axis of rotation, we subtract the X %Y Z coordinates from their transformation Matrices Vw1=[T11(1,4)T10(1,4);T11(2,4)T10(2,4);T11(3,4)T10(3,4)]; Vw=cross(Vw1,n); %Finding the angle between the two vectors the=acos(dot(Vp,Vw)/(norm(Vp)*norm(Vw))); WMRA_OR %###################################################################### #### % This M file creates optimized parameters for the weighted matrix values % of the wheels to account for rotation during the % execution of a given trajectory. % Function Declaration function W1=WMRA_OR(the,i,n,bmax) %if atan2(sin(the),cos(the))~=0 %W1=1; %elseif atan2(sin(the),cos(the))<0.3 %W1=10; bmin=bmax; W1=1/(((bmaxbmin)^2*(2*thebmaxbmin))/(4*(bmaxthe)^2*(thebmin)^2)); end WMRA_VR_Animation2 % This function does the animation of USF WMRA with 9 DOF using Virtual Reality Toolbox. % Function Declaration: function WMRA_VR_Animation2(i, Twc, q) % Declaring the global variables:

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Appendix B (continued) 132 global L WMRA % The initialization of the animation plot: if i==1 % Reading the Wheelchair's constant dimentions, all dimentions are converted in millimeters: L=WMRA_WCD; % Opening the WMRA file: WMRA = vrworld(' \ 9_wmra.wrl'); open(WMRA); % Changing the View Point of the simulation: WMRA.DynamicView.translation=[Twc(1,4) 0 Twc(2,4)]; % Calculating the wheelaxle transform instead of the arm base transform: Twc=Twc*[eye(3) L(2:4) ; 0 0 0 1]; % The orientation about Z of the wheelchair: phi=q(9); % Calculating wheelchair's wheels' angles: ql=q(8)/L(5)L(1)*q(9)/(2*L(5)); qr=q(8)/L(5)+L(1)*q(9)/(2*L(5)); % Updating the VRML file for the new angles and distances: WMRA.Chair.translation=[Twc(1,4) Twc(2,4) L(5)]; WMRA.Chair.rotation=[0 0 1 phi]; WMRA.LWheel.rotation=[0 1 0 ql]; WMRA.RWheel.rotation=[0 1 0 qr]; WMRA.ARM2.rotation=[0 0 1 q(1)]; WMRA.ARM3.rotation=[0 1 0 q(2)]; WMRA.ARM4.rotation=[0 0 1 q(3)]; WMRA.ARM5.rotation=[0 1 0 q(4)]; WMRA.ARM6.rotation=[0 0 1 q(5)]; WMRA.ARM7.rotation=[0 1 0 q(6)]; WMRA.ARM8.rotation=[0 0 1 q(7)]; % Viewing the simulation: view(WMRA); % Closing the animation plot: elseif i==3 close(WMRA); delete(WMRA); % Updating the animation plot: else WMRA.DynamicView.translation=[Twc(1,4) 0 Twc(2,4)]; Twc=Twc*[eye(3) L(2:4) ; 0 0 0 1]; phi=q(9); ql=q(8)/L(5)L(1)*q(9)/(2*L(5)); qr=q(8)/L(5)+L(1)*q(9)/(2*L(5)); WMRA.Chair.translation=[Twc(1,4) Twc(2,4) L(5)]; WMRA.Chair.rotation=[0 0 1 phi]; WMRA.LWheel.rotation=[0 1 0 ql]; WMRA.RWheel.rotation=[0 1 0 qr]; WMRA.ARM2.rotation=[0 0 1 q(1)]; WMRA.ARM3.rotation=[0 1 0 q(2)];

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Appendix B (continued) 133 WMRA.ARM4.rotation=[0 0 1 q(3)]; WMRA.ARM5.rotation=[0 1 0 q(4)]; WMRA.ARM6.rotation=[0 0 1 q(5)]; WMRA.ARM7.rotation=[0 1 0 q(6)]; WMRA.ARM8.rotation=[0 0 1 q(7)]; end