Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2008 Modeling and Simulation of Skid Steered Robot Pioneer 3AT Dhanashekar Arcot Krishnamurthy Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] FLORIDA STATE UNIVERSITY COLLEGE OF ENGINEERING MODELING AND SIMULATION OF SKID STEERED ROBOT PIONEER – 3 AT By DHANASHEKAR ARCOT KRISHNAMURTHY A Thesis submitted to the Department of Mechanical Engineering In partial fulfillment of the requirements for the degree of Master of Science Degree Awarded: Spring Semester, 2008 The members of the Committee approve the Thesis of Dhanashekar Arcot Krishnamurthy defended on March 27th, 2008. ________________________________ Patrick Hollis Professor Directing Thesis ________________________________ Carl Moore Committee Member ________________________________ Juan Ordonez Committee Member Approved: ___________________________________ Chiang Shih, Chair, Department of Mechanical Engineering ___________________________________ Ching-Jen Chen, Dean, College of Engineering The Office of Graduate Studies has verified and approved the above named committee members. ii ACKNOWLEDGEMENTS I would like to take this opportunity to thank a few of the many people who have made my graduate studies and this thesis possible. First of all, I would like to thank my advisor Dr. Patrick Hollis for his valuable guidance and support. I would also like to extend my gratitude to Dr. Emmanuel Collins who gave me an opportunity to work with the CISCOR group in the mechanical engineering department. I would like to thank Dr. Juan Ordonez and Dr. Carl Moore, for serving in my graduate committee. Special thanks to Wei and Oscar, whose work with the Pioneer 3AT torque controller made running the robot test runs possible. Also, I thank the other members of the CISCOR group, for support and help in the research. I owe special gratitude to a number of close friends here in Tallahassee. They made my stay pleasant and enjoyable. Finally, I’m thankful to my family and friends back home in India. They give me the strength and courage to face and overcome new challenges. iii TABLE OF CONTENTS List of Tables ..................................................................................... v List of Figures ..................................................................................... vi Abstract .......................................................................................... viii 1. Introduction and Background ............................................................ 1 1.1 Autonomous ground vehicle .................................................... 1 1.2 Purpose and organization of the thesis .................................... 2 1.3 Steering mechanisms .............................................................. 4 1.4 Vehicle dynamic modeling ....................................................... 7 1.5 Pioneer 3AT and Torque controller........................................... 10 2. Physical parameter determination ..................................................... 13 2.1 Center of mass ......................................................................... 14 2.2 Moment of inertia ..................................................................... 18 2.3 Friction and rolling resistance coefficient ................................. 24 3. Mathematical Modeling ..................................................................... 26 3.1 Theoretical model .................................................................... 26 3.2 Robot test-runs ........................................................................ 34 3.3 Simulations using MATLAB ..................................................... 38 4. Simulation using ADAMS .................................................................. 43 4.1 ProE model of Pioneer 3AT ..................................................... 43 4.2 Modeling and analysis ............................................................. 45 5. Conclusions and future work.............................................................. 54 APPENDICES ..................................................................................... 55 A MATLAB code for simulation of robot ....................................... 55 REFERENCES ..................................................................................... 60 BIOGRAPHICAL SKETCH …..…………………………………………… 61 iv LIST OF TABLES Table 2.1: Weights of different parts ...................................................... 23 Table 2.2: Oscillation time ...................................................................... 23 Table 2.3: Moment of inertia values of the robot .................................... 23 v LIST OF FIGURES Figure 1.1: Independent steering system .............................................. 4 Figure 1.2: Single axis system .............................................................. 5 Figure 1.3: Skid steered system ............................................................ 6 Figure 1.4: Axis system ......................................................................... 7 Figure 1.5: Forces acting on the wheel ................................................. 8 Figure 1.6: Pioneer 3AT ........................................................................ 10 Figure 2.1: Robot reference axis system .............................................. 13 Figure 2.2: Weighing the robot .............................................................. 14 Figure 2.3: Weight distribution .............................................................. 15 Figure 2.4: Position of CG ...................................................................... 16 Figure 2.5: CG in Z direction ................................................................. 17 Figure 2.6: Hanging weight ................................................................... 18 Figure 2.7: Experimental 4 wire setup ................................................... 20 Figure 2.8: Three Wire setup ................................................................ 21 Figure 2.9: ‘x’ and ‘y’ axes setup ............................................................ 22 Figure 2.10: Friction coefficient ............................................................. 25 Figure 3.1: SAE vehicle axis system ..................................................... 26 Figure 3.2: Free body diagram .............................................................. 28 Figure 3.3: Robot test runs – straight line motion ................................. 35 Figure 3.4: Robot test runs – curve motion ........................................... 36 Figure 3.5: Robot test runs – inclined plane motion .............................. 37 vi Figure 3.6: Simulation result – straight line motion ............................... 39 Figure 3.7: Robot path for curve motion ................................................ 40 Figure 3.8: Simulation result – curve motion ......................................... 41 Figure 3.9: Simulation result – inclined plane motion ............................ 42 Figure 4.1: CAD model of Pioneer 3 AT ................................................ 43 Figure 4.2: Front and side view of ProE model ..................................... 44 Figure 4.3: ADAMS wireframe model .................................................... 45 Figure 4.4: ADAMS straight line motion ................................................ 46 Figure 4.5: Velocity in forward direction ................................................ 47 Figure 4.6: Velocities from robot straight line run ………………………… 47 Figure 4.7: Robot path for curved motion .............................................. 48 Figure 4.8: ADAMS inclined plane motion ............................................ 49 Figure 4.9: Robot circular path on a flat plane ....................................... 50 Figure 4.10: Robot circular path on an inclined plane ............................ 51 Figure 4.11: Robot circular path on a declined plane ............................. 51 Figure 4.12: Velocities in X and Y direction-flat plane ........................... 52 Figure 4.12: Velocities in X and Y direction-inclined plane ................... 53 Figure 4.13: Velocities in X and Y direction-declined plane .................. 53 vii ABSTRACT Mobile robots are used extensively for their ability to navigate and perform tasks in unstructured environments, without continuous human guidance. They are used for space exploration, military surveillance, nuclear power industry, security, etc. Before these robots are put to work, they need to be tested under different conditions. While developing or testing these robots, it is important that one models the actual vehicle and simulates test conditions similar to the actual ones. These models give an idea of how the robot is going to behave and thus play a critical role in the development of the vehicle navigation and control systems. For a skid steered robot like the Pioneer 3AT, the velocity constraints are quite different from other mobile platforms, because the wheels must skid laterally to follow a curved path. This implies that the control of this robot at the kinematic level only is not sufficient and, in general, demands the use of a dynamic model. This thesis develops a mathematical model of a 4-wheel skid- steering mobile robot, the Pioneer 3AT. The model is validated with actual experiments on the Pioneer 3AT and also modeling and simulation using Pro Engineer