Navigation and control of indoor mobile manipulator

System Modeling 2.1 The Overall System of Mobile Manipulator 17 2.3 Dynamic Modeling of Mobile Platform and its Properties 26 2.4 Dynamic Modeling of Manipulator and its Properties 28 2.

Thesis for the Degree of Doctor of Philosophy

Navigation and Control of Indoor Mobile Manipulator

by Tan Lam Chung Department of Mechatronics Engineering

The Graduate School Pukyong National University

February 2006

Navigation and Control of Indoor Mobile Manipulator

실내 이동 매니퓰레이터의 항해와 제어

by Tan Lam Chung

Supervisor: Professor Sang Bong Kim

A thesis submitted in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

In Department of Mechatronics Engineering, the Graduate School,

Pukyong National University

February 2006

Navigation and Control of Indoor Mobile Manipulator

A Dissertation

by

Tan Lam Chung

Approved of styles and contents by:

Chairman Yeon Wook Choe

Member Ki Sik Byun Member Sang Bong Kim

Member Sae Jun Oh Member Young Bok Kim

February 2006

Acknowledgments

And there come a day when I have to leave Korea, still there be joy and sorrow to get the commencement of life The helps and continuous supports from professors, colleagues, friends, and family to whom I am most grateful make me mature Without you, all of you, I am not to be what I am today I would like to thank each of you individually by word, but I do so in my heart

First of all, I would like to thank Professor Sang Bong Kim, my supervisor with a spirit of enterprise, who helped me to find my path and has been providing continual support, advices, and wonderful research opportunities during my studying I promise that I will do my utmost in the future for a better work to come in my country and in here as well

I would like to thank the members of my thesis committee: Prof Yeon Wook Choe, Prof Ki Sik Byun, Prof Sae Jun Oh and Prof Young Bok Kim who have provided wonderful feedback on my work and great suggestions for the better contribution of my thesis Specially, thanks to Prof Myung Suk Lee at Department of Microbiology for her care to me and Vietnamese community in Pukyong National University as well, and Prof Hwan Seong Kim in Korea Maritime University for the supports to Vietnamese students

I would like to thank Assoc Prof Hoai Quoc Le, who had given me a precious support and knowledge base before I left for Korea; Dr Huu Loc Nguyen for the recommendation; Dr Tan Tien Nguyen, who introduced me a good chance of study in CIMEC Lab and the initial ideas; Dr Tan Tung Phan and

Dr Thien Phuc Tran, who give me a lot of precious advices in the academic and

practical field, Dr Hak Kyeong Kim and Dr Jin Ho Suh, who have a major role played in this study, both in their lectures and in life; MSc Son Ngoc Hoang Tran

in Korea Maritime University for the useful technical discussion

I am grateful to all members of CIMEC Lab for giving me a comfortable and active environment to achieve my work: Dr Gun You Lee, Dr Byoung Oh Kam, Dr Hur Churl, Dr Trong Hieu Bui, Manh Dung Ngo, Thanh Phuong Nguyen, Hoang Duy Vo, Sang Kwun Jeong, Seung Mok Shin, Soung Jae Park, Suk Yoel Kim, Sung Wook Kim, Won Ki Lee, Jae Sung Im, Young Kyu Kim, Sung Jin Ma, Hee Suk Lee, Sang Chan Kim, Ba Da Park, Byung Yong Kim, Hak Cheol Lee, Joon-Ho Jeong, Suk Min Yoon, Do Kyung Lee, Nak Soon Choi, Dae Won Kim, Kyong Soo Kim, Gun Baek Lee You all, by this way or another one, have helped me a lot during the time of my study here Also, thanks to Vietnamese students: Thanh Tong Phan, Minh Tam Nguyen, My Le Du, Thuy Duong Nguyen, Chanh Luan Huynh, Thi Tham Pham, Tat Hien Le, Manh Vu Tran in Pukyong National University; Tuong Long Nguyen, Duy Anh Nguyen, Thanh Dao Tran in Korea Maritime University for their abroad friendly atmosphere; Phuong Hoang Anh Nguyen, Xuan Phu Tran and all my friends in Vietnam for their encouragement

Warmly thanks to my parents, my sisters, my brother, my nieces and nephews, my uncles and my loved ones; the patience, support, and impeccable understanding allowed me to write this thesis

Pukyong National University, Pusan, Korea

December 26, 2005

The precious thing in this life is understanding and sympathy

To my parents

Chung Van Ho – Le Ngoc Chon

2 System Modeling

2.1 The Overall System of Mobile Manipulator 17

2.3 Dynamic Modeling of Mobile Platform and its Properties 26 2.4 Dynamic Modeling of Manipulator and its Properties 28 2.5 Kinematic Model for the Mobile Platform 29 2.5.1 Kinematics Model for Path-Following of Mobile Platform 30 2.5.2 Kinematics Model for Tracking Problem of Mobile Platform 33 2.6 Lyapunov Function for the Mobile Platform 36 2.7 Lyapunov Function for the Manipulator 37 2.8 Lyapunov Function for the Mobile Manipulator 38

3 Indoor Navigation of Mobile Manipulator

3.1 General Environment Model for Mobile Robot Navigation 42 3.2 General Problem of Path Planning for Mobile Platform 44

3.3.1 Convex Hull - Graham’s Algorithm 46 3.3.2 Visibility Graph Construction - Brute Force’s Algorithm 50

3.3.3 Shortest Path Finding- Dijkstra’s Algorithm 52

3.4.2 Simulation Results of Cubic Spline Algorithm 58 3.4.3 Convert Cartesian Trajectory to Joint Space 62

5.1 Robust Damping Controller for the Mobile Manipulator 80

5.2.1 The Simulation for the Mobile Platform 86 5.2.2 The Simulation for the Manipulator 87

6 System Implementation

6.3.1 Mobile Manipulator Implementation 117

6.4.1 Experimental Results for the Mobile Platform 121

6.4.2 Experimental results for the manipulator 125

Appendix B Recursive Newton-Euler Motion Equation of Manipulator 153

Appendix E: Proof of Theorem 5.1 158

List of Figures

Fig 1.2 Service robot Helpmate for hospital transportation 3

Fig 1.4 PeopleBot with a griper and a camera for service tasks 5

Fig 1.5 PowerBot with a high payload manipulator 6

Fig 2.5 Kinematic analysis for path-following problem 30

Fig 2.6 Kinematic analysis for trajectory tracking problem 33

Fig 2.7 Tracking control structure of the mobile manipulator 41

Fig 3.2 Illustration of motion planning for mobile robot 45

Fig 3.4 The algorithm for checking a point on the left of a line 48

Fig 3.5 The resulting sorted point in stack points 48

Fig 3.8 The illustration of reduced visibility graph 51

Fig 3.10 Dijkstra and cubic spline algorithm implementation 55

Fig 3.11 Cubic spline of position 59

Fig 3.14 3D Cubic spline 61

Fig 3.15 Cubic spline implementation 61

Fig 4.1 Pin-hole camera model 65

Fig 4.2 Calibration pattern image and correspondence detection 72

Fig 4.3 Camera calibration test bed 75

Fig 4.4 Camera user interface 75

Fig 4.5 Object detection scheme 77

Fig 4.6 Finding bounding box 77

Fig 4.7 Conner detection scheme 78

Fig 5.1 Block diagram of robust damping controller 83

Fig 5.2 Cubic spline reference trajectory for platform 88

Fig 5.3 Reference trajectory parameters for platform 88

Fig 5.4 Platform tracking errors for full time 89

Fig 5.5 Platform tracking errors for the initial time 89

Fig 5.6 Velocities of platform’s center 90

Fig 5.7 Wheel velocities 90

Fig 5.8 Robust vector of mobile platform 91

Fig 5.9 Wheel’s torques of mobile platform 91

Fig 5.10 Tracking trajectory of mobile platform (2s) 92

Fig 5.11 Tracking trajectory of mobile platform (8s) 92

Fig 5.12 Joint reference trajectory 93

Fig 5.13 Tracking position of joint 1 93

Fig 5.14 Tracking position of joint 2 94

Fig 5.15 Tracking position of joint 3 94

Fig 5.16 Tracking position of joint 4 95

Fig 6.1 Configuration diagram of the overall control system 99

Fig 6.2 Device pin-out of the USB controller FT245BM 101

Fig 6.24 The experimental mobile manipulator 121

Fig 6.25 Reference trajectory simulation for the experiment 122

Fig 6.28 Tracking error simulation of mobile platform 123

List of Tables

Table 5-1 Data point for cubic spline reference trajectory 84

Table 5-2 Numerical values of the mobile manipulator for simulation 85

Navigation and Control of

Indoor Mobile Manipulator

A Dissertation by

Tan Lam Chung

Department of Mechatronics Engineering, Graduate School

Pukyong National University

Abstract

A mobile manipulator is a system composed of a manipulator attached to a mobile base Such a combined system is capable of performing manipulation task

in much larger workspace than a fixed-based manipulator

In this thesis, a system of a two-wheeled mobile platform and a six-dof elbow manipulator is considered It is controlled to follow a planned curved trajectory and pick an object in the 3D workplace using USB camera There are several works that have been done to meet the above demand as follows:

The dynamic equation of the mobile manipulator is established taking into account system uncertainties, disturbances and the interactions between the mobile platform and the manipulator Also, several properties and assumptions of bounded parameters are presented which is needed for the controller design stage

To be useful in the real world, a mobile manipulator should be able to navigate safely in an environment and accomplish given tasks despite unexpected changes in its surroundings Motion planning for the mobile robot navigation is considered The motion planning is composed of two steps: path planning and trajectory planning To do such the task, first, the reduced environment is modeled and represented by means of the visibility graph, then the shortest path is obtained using Dijkstra’s algorithm The path becomes smooth using cubic spline interpolation

To control the system, robust damping controller is applied to evaluate the behavior of the system model and to compensate the nonlinear terms in the system dynamics taking into account the uncertainties and disturbance and the interaction between the two subsystems The control laws are derived based on robust damping coefficient and the sensory data to make quick converge to the stable state of the total closed-loop system The effectiveness of the robust control scheme and the estimation method are to be verified by the simulation and experimental results In the design process, an USB camera is used to detect the object’s coordinates in 3D space A practical camera calibration based on Tsai’s method is applied to find the camera parameters These parameters are, in turn, used to compute the relative position between the camera and the object which is needed for the path planning scheme Also, a combined system which composed

of a computer and a multi-dropped PIC-based controller is implemented using USB-CAN communication to meet the control demand of the whole system The simulation and experimental results have been given to show the effectiveness of the proposed model and the robust controller and its application for the practical fields

x− the fixed coordinate system on the mobile platform

C center of mass of the mobile platform

w

wheel of the mobile platform [m]

)

,

(x y center coordinates of the mobile platform [m]

φ heading angle of the mobile platform [rad]

v linear velocity at center of the mobile platform [m s]

ω angular velocity at center of the mobile platform [rad s]

W intersection of wheel axes and the reference path

ω reference angular velocity [rad s]

q generalized coordinate vector of the mobile manipulator

E input transformation matrix

λ Lagrange multiplier, or vector of constraint forces

the wheel axis [kg.m2]

m

I moment of inertia of each wheel with its motor around

the wheel diameter [kg.m2]

c

I moment of inertia of the body around the vertical axis

through the mass center of the mobile platform [kg.m2]

η velocity input vector of the mobile platform [m/s]

η desired velocity input vector of the mobile platform [m / ] s

ηˆ velocity error of the mobile platform [m / ] s

)0

( w−X w Y w Z w world space coordinate system

d distance two adjacent sensor element iny-axis [mm / sel]

R extrinsic camera parameter - rotation matrix

T extrinsic camera parameter - translational matrix

1

Introduction

The design of intelligent autonomous machines to perform tasks that are dull, repetitive, hazardous, or that require skill, strength, or dexterity beyond the capability of humans is the ultimate goal of robotics research Examples of such

tasks include manufacturing, excavation, construction, undersea, space and planetary exploration, toxic waste cleanup, robotic assisted surgery and so forth Therefore, robotics research is highly interdisciplinary requiring the integration of control theory, mechanics, electronics, artificial intelligence and sensor technology

1.1 State of the Art

The earliest applications of robots were in materials handling, spot welding, and spray painting Robots were initially applied to jobs that were hot, heavy, and hazardous such as die casting, forging, and spot welding [1] Especially, arc welding, which is potentially a large application for robots, places high demands

on the technology During the time that industrial welding robots have been in use,

the revolute manipulator has become by far the most popular for arc welding The reason for the popularity of the jointed arm type is that it allows the welding torch

to be manipulated in almost the same fashion as a human being would manipulate

it A commercial arc welding robot of KUKA is shown in Fig 1.1 [2]

Fig 1.1: Arc welding robot of KUKA

Helpmate Robotics has developed a navigational technology needed to

create mobile robots that can scurry around a hospital or other industrial

environment They are delivering medicines, supplies, prepared food,

x-ray images and other material in about 100 hospitals in the United States and Canada (Fig 1.2) [2] Helpmate researchers successfully developed a sensor which

improved light direction and range scanner The sensor is a device in the eyes of

the robot that senses light, calculates direction, and determines the range to objects

in its path This is a clear advance over previous technology, which used sonar to detect shapes Researchers also developed navigation capabilities based on new sensing systems and ways of combining data from different sensors These capabilities permit the control of robots in quasi-structured environments - places with predefined components such as doorways, light fixtures, windows, and elevators that are fixed in place and definable from photos or engineering drawings and among objects that are not predefined, such as a patient on a gurney and human workers moving about the space

Fig 1.2: Service robot Helpmate for hospital transportation

In Fig 1.3, Robot ROV Tiburon for underwater archaeology with

tele-operated control is used by MBARI (Monteray Bay Aquarium Research Institute) for deep-sea research This UAV (Unmanned Arial Vehicle) provides autonomous hovering capabilities for the human operator

Fig 1.3: ROV Tiburon UAV

If one looks for an autonomous system which can perform service tasks, behavior-based system can be found very often This system allows a certain level

of autonomy but do not obtain a good reliable positioning PeopleBot was developed by ActiveMedia Robotics as shown in Fig 1.4 It provides a mobile

base with a gripper and a precise pan-tilt camera for sensing and grasping objects

to do service activities It uses state machines to recognize a colored object, fetch

it from one table and set it on another place Such a service task does not require millimeter accuracy; it needs a reactive behavior in the manner of “cup not above table yet, move a bit forward” In this case, results in the shape of objects do not play a role for this kind of positioning strategy

Fig 1.4: PeopleBot with a griper and a camera for service tasks

PowerBot is another robot by ActiveMedia Robotics shown in Fig 1.5 This

robot is composed of a mobile platform and a manipulator for a payload of about 100kg This system is controlled with a behaviour-based approach Still, a lot of questions have to be answered until they are suitable to fulfill industrial application It should be mentioned that behavior-based robotics is still at the beginning of its development Most of the systems are built for scientific purposes only The above mentioned disadvantage of low position reliability prevents these systems from being used in industry

Fig 1.5: PowerBot with a high payload manipulator

A shrimp robot has been developed by ASL – Autonomous System Lab as

shown in Fig 1.6 The shrimp robot with its climbing ability is extraordinary in comparison to most robots of similar mechanical complexity The flexibility of its

motion is owns much to the specific geometry and the manner in which the center

of mass of the robot shifts with respect to the wheels over time

Fig 1.6: SHRIMP robot

1.2 Background and Motivation

The primary task of a robot manipulator is the motion control that requires the accurate positioning, such as, carrying an object, painting a surface or welding, and many fundamental theory problems in its motion control are solved At the early stage, the major position control of the manipulator is known to be the computed torque control, or inverse dynamic control: each joint is decoupled and linearized based on the estimated dynamic models; therefore, the positioning performance of this control is mainly dependent upon the accurate estimations of the dynamics equation Spong and Vidyasaga [3] (1989) designed a controller based on the computed torque control for manipulators The idea of this control is

to exactly linearizes all of the coupling nonlinearities in the Lagrangian dynamics

in the first stage so that the compensator can be designed based on linear and decoupling plant in the second stage, for example, the method of stable factorization for the robust feedback linearization problem [4] (1985) Also, several techniques can be used in the second stage Corless and Leitmann [5] (1981) proposed a theory based on Lyapunov’s second method to guarantee the stability

of the uncertain manipulator system In practice, it is true that exact estimation of robot dynamic models is not possible so that the positioning performance is deteriorated; additionally, the control performance is also subjected to the uncertainties in mechanical manipulator itself It is proper to say that the nonlinear

control is suitable for such the nonlinear dynamical system, that is, adaptive

control and robust control Adaptive control has proven successful in dealing with

modeling uncertainties in general nonlinear systems by online tuning of parameters, but this control cannot be utilized to estimate a system with fast time-varying uncertainties And robust controller is the candidate that can be applicable for this case totally; it can stabilize nonlinear systems with arbitrary fast time-varying uncertainties or parameters, for this technique requires only known bounding functions of the uncertainties It can be seen that the applications of manipulator have gotten a success in practical fields, but still most of them that exist nowadays are based on a fixed platform Yet, these applications suffer from a

fundamental disadvantage: lack of mobility [2] The mobile robots have shown the

effectiveness and flexible solution for such disadvantage

In contrast to the manipulator, mobile robotics has been a recent field In fact, the manipulators and the mobility are studied in parallel but not together for a long time; this fact made them limited in the applications For example, a mobile robot autonomously delivers parts between various assembly stations by following special electrical guide wires using a custom sensor; a cleaning robot takes advantage of the regular geometric pattern of aisles in supermarkets to facilitate the localization and navigation for the service tasks The examples show a viewpoint of application fields that are the case of applying the mobile robot effectively

Among the mobile robot community, a two-wheeled mobile robot is one of the well-known systems with nonholonomic constraints In literature, some nonlinear feedback controllers have been proposed to solve these problems Kanayama et al [6] (1991) proposed a stable tracking controller for determining linear and angular velocities of a nonholonomic vehicle using Lyapunov function

C Canudas de Wit et al [7] designed three nonlinear control laws to stabilize the

motion of the mobile robots for three problems: trajectory tracking, path following and point stabilization These controllers, however, are considered under the

kinematics model only and assumed that perfect velocity input is guaranteed Some other controllers have been designed in which the dynamics of the mobile robot is considered to achieve the perfect velocity control input Fierro and Lewis

[8] (1998) presented a neural network-based robust adaptive control scheme for practical point stabilization of a nonholonomic mobile robot This scheme provides combined kinematics/torque control with guaranteed stability via Lyapumov method The control scheme is applicable to tracking and path following problems Due to the neural network learning ability, it does not require any priori information on the robot dynamics parameters J M Yang, and J H Kim [9] (1999) proposed a sliding mode control law which is robust against initial condition errors, measurement disturbances and noise in the sensor data to asymptotically stabilize the mobile robot’s posture to a desired trajectory by means of the computed-torque method In these methods, however, perfect knowledge about the parameter value of the mobile robot is necessary Therefore, some other controllers have been proposed based on adaptive and robust control Fukao et al [10] (2000) dealt with the adaptive tracking control of a two-wheeled mobile robot Corradini et al [11] (2001) proposed a sliding mode tracking controller for the dynamic model of a two-wheeled mobile robot in the presence of uncertainties, both parameter variations and input disturbances based on the boundedness of the uncertainties

The science makes quick progress, and the mobile manipulators, the combination of the above systems, have become popular in applications These systems, in one sense, are considered to be as human body, so they are applicable

in many practical fields for industrial automation, public services and home

entertainment In literature, mobile manipulators have been and will be attractive

to the researchers worldwide that make this field so rich Yamamoto et al [12](1994) addressed the motion between the base and the manipulator and the problem of following a moving surface Liu and Lewis [13] (1990) developed a decentralized robust controller for trajectory tracking of the mobile manipulator end-effector Lin and Goldenberg [14] (2002) developed robust damping controller for the positioning control of mobile manipulator with unknown dynamics and disturbances and do the experiment for a fixed-base 2-link manipulator

Additionally, to be useful in the real world, a mobile manipulator should be able to navigate safely in an environment and accomplish given tasks despite unexpected changes in its surroundings Navigating mobile robots find diverse applications today such as in automated freeway driving, cleaning of hallways, exploration of dangerous regions and as aids for convalescing patients In future robots are envisioned to assist people in day to day life and this has lead to a growing research in the areas of cooperative robotics, human robot interaction and personal robotics There are two courses of robot architecture developing:

behavior architecture and precision architecture If behavior architecture is used,

it is difficult to perform a precise positioning of the mobile platform and vice versa

In a lot of cases, a reasonable trade-off between flexible behavior and precision is not possible Let’s assume a robot has to perform the task of moving from point 1

to point 2 One standard solution is to calculate the exact trajectory and control the

robot follows it If the robot comes across an obstacle on its journey it has to find a path around it, which means it has to leave the original plan at least for a while It might be reasonable to use an avoid-obstacle behavior for that But who can decide when to switch off a precise algorithm and when to use a behavior or how

to mix them? These questions are focal points of current research interests Even more problems occur when a mobile robot carries a manipulator

1.3 About This Work

It can be seen that how to exactly model, efficiently control the motion of a mobile manipulator and interact with its surroundings in a structured environment

is still an open question in robotics

This thesis studies about the navigation and control of a mobile manipulator for indoor environment The mobile manipulator has to perform a pick-and-place task to an object for a long distance in a structured environment such as office or house The environment is modeled as simple as a set of convex polygon so that the graph theory can be applied for motion planning: a tractable collision-free path

is realized for the mobile platform using a shortest path algorithm; then the path is smoothened using an interpolation algorithm in accordance with natural behavior

of the mobile platform The convex polygons can be considered as obstacles as well The task is composed of two stages: first, the mobile platform moves from the initial configuration to the goal configuration; second, as the mobile platform reached the goal, the manipulator, in turn, pick an object and place on a specified

position of it To control the system, a robust damping controller based on the work of [14] is applied for the tracking problem to the mobile manipulator taking into account system uncertainties, disturbance and the interaction between the two subsystems In the system a USB camera was implemented to detect the coordinate of the object in 3D space with respect to the coordinate of the manipulator so that the task is performed with the acceptable accuracy The camera calibration method is based on the work of [15], which is among the success method in practice What’s more, a combined control system which is composed of a computer and a multi-dropped PIC-based controller is developed using USB-CAN communication to meet the demand of the whole system It should be noticed that, in the practical fields, there are two different types of work

considered for the mobile manipulator: (1) Stationary work - the mobility is used

to transport the manipulator from a place to another place where then a specific

task is executed; (2) Continuous work - the task is done during the motion of the

mobile platform This thesis concentrates on the first work only; the result of the thesis can be extended to the second one with several modifications of tracking

control laws, environment modeling based on object-oriented programming method, sensor fusion implementation and client-server communication

architecture

This thesis consists of seven chapters to meet the above objective The content and summary of contribution in each chapter is as follows:

Chapter 1: Introduction - Present related studies in literatures and practical field,

the motivation of this research, and the outline of contents with summary of contribution

Chapter 2: System Modeling - Present a model of the mobile manipulator which

is composed of a two-wheeled mobile platform and a six-dof manipulator The dynamic equation of the combined system is shown taking into account the system uncertainties, disturbances and the interaction between the two subsystems Several properties are also derived from such the dynamic model Two kinematics control scheme is presented to give the desired velocity controller: path following and trajectory tracking controllers Also, three Lyapunov function equations are defined for the mobile platform, the manipulator and the whole mobile manipulator with the separated nonlinear terms which are needed for the robust controller design stage

Chapter 3: Indoor Navigation for Mobile Manipulator - Design the

trajectories for mobile platform which satisfy the constraints of the environment First, the environment is bound with obstacles of convex polygons The convex hull of the obstacles is identified using Graham algorithm, then V-Graph is built using Brute-Force algorithm and the shortest path is found using Dijkstra’s algorithm The 3D

cubic spline is applied to such the trajectory for smooth and shortest way Additionally, the cubic spline is applied for the trajectory planning of the manipulator as well The simulations of position, velocity and acceleration have been done to illustrate the interpolation algorithm The simulation has been done to verify the algorithm

Chapter 4: Camera Localization – In this chapter, a camera calibration method

is implemented based on T.Sai’s method: mono-view coplanar points method The camera parameters are introduced and computed

to verify the calibration results These parameters are, in turn, used

to derive the camera posture which is needed for the path planning scheme of the system The experiment has been done to show the effectiveness of the calibration method

Chapter 5: Robust Control of Mobile Manipulator – A nonlinear tracking

controller based on the robust damping control is applied to a wheeled mobile platform and a six-dof manipulator The combined system is considered in terms of dynamic model taking into account uncertainties and disturbances The controller are tuned with the control gain, to guarantees the stability of the closed-loop system and the global uniform boundedness of all tracking errors The simulation results have been done to show the effectiveness of the controller

two-Chapter 6: System Implementation – In this chapter a control solution which is

a combination of computer and microcontroller is developed The control system is composed of a master USB-CAN module which connects to eight slave servo-CAN modules using CAN communication and link to computer using USB communication Several user interfaces on computer are developed to get control performance effectively: USB-CAN interface, USB camera interface, Servo-CAN interface, manipulator controller interface and motion planning interface A DC motor model is given, and cascade position control applied to the Servo-CAN is presented The experimental combined system of 6-dof manipulator and a two-wheeled mobile platform has been made The experimental results is given to show the possibility of the proposed the system model and the robust controller as well

Chapter 7: Conclusions and Future Works - The results of this thesis are

summarized and several capabilities are proposed for both the platform and manipulator to make it flexible in the practical field Again, control makes robots useful in application A robust controller integrated in a microcomputer with a camera can efficiently control the motion

of the mobile manipulator along the desired trajectory and forces it exerts upon its structured environment These are to be presented in the following chapters

2.1 The Overall System of a Mobile Manipulator

First, consider a two-wheeled mobile platform which can move forward, and spin about its geometric center, as shown in Figure 2.1

C P

(a)

(b) Fig 2.1: Geometry of the mobile platform: (a) 2D geometry; (b) 3D model

The length between the wheels of the mobile platform is 2band the radius

of the wheels is r w {OXY} is the stationary coordinates system, or world coordinates system; {Pxy is the coordinates system fixed to the mobile robot, and }

of the mobile platform and placed in the x-axis at a distance d from P ; the length

of the mobile platform in the direction perpendicular to the driving wheel axis is

a and the width is L The balance of the mobile platform is maintained by a small

castor whose effect shall be ignored It is assumed that the center of mass Cand

the origin of stationary coordinate P are coincided

Second, the manipulator used in this thesis is of an articulated-type manipulator with two planar links in an elbow-like configuration: three rotational joints for three degrees of freedom They are controlled by dedicated DC motors Each joint is referred as the waist, shoulder and arm respectively Also, the manipulator has a 3-dof end-effector function as roll, pitch and yaw; and a parallel gripper attached to the yaw

The length and the center of mass of each link are presented as(L b1,Z b1), )

,

(L b2 Z b2 , (L b3,Z b3), (L b4,Z b4), (L b5,Z b5), respectively The geometric model the coordinate and the dimensions for each link are shown in Fig 2.2

Link 2 Shoulder

Link 1 Waist

Z7

X1 Z0

In this thesis, the mobile manipulator is of a holonomic manipulator on the nonholonomic mobile platform The control problems of such the mobile manipulator cannot be solved by traditional methods due to the nonholonomic nature of the system which is imposed by the platform’s wheels Moreover, the mobile manipulator possesses a complex and strongly coupled dynamic model of the nonholonomic dynamics of the mobile platform and the dynamics of the manipulator The block diagram of the whole control system to solve the above problem is shown in Fig 2.3

Manipulator

Mobile Platform

Trajectory Planning Motion Planning

Desired Trajectory

Mobile Platform Controller

Signal Processing

Wireless Sensors

Fig 2.3: Block diagram of the mobile manipulator control

The motion control problem is generally decomposed into three stages: