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Development of Kinematic and Dynamic Models for the Argo J5 Rover

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Development of Kinematic and Dynamic Models for the Argo J5 Rover Development of Kinematic and Dynamic Models for the Argo J5 Rover by Erin J. E. Austen A thesis submitted to the Faculty of Graduate and Postdoctoral Affairs in partial fulfillment of the requirements for the degree of Master of Applied Science in Aerospace Engineering Department of Mechanical and Aerospace Engineering Carleton University Ottawa, Ontario © 2019 Erin J.E. Austen Abstract Planetary exploration rovers are the most efficient means of off-world surface exploration. As mobile laboratories, they are used to perform various experiments and gather data semi-autonomously from remote extraterrestrial environments, both for planetary science and assessing conditions in preparation for human exploration. To accomplish the mission and access sites of scientific interest, the rover must be able to traverse various types of unstructured terrain without becoming embedded or succumbing to other hazards. Modelling of the rover is essential to understand how the rover interacts with its environment and how to select the best path. This thesis presents the development of three-dimensional kinematic and dynamic models, using MATLAB and SimMechanics, describing the Argo J5 four-wheel rover, in response to terrain elevation inputs and slip. The kinematic models describe the pose and velocity of the rover using the Denavit-Hartenberg convention, while the SimMechanics dynamic model is combined with a terramechanics model to develop accelerations and obtain the forces and torques, based on terrain properties. The kinematic analyses were performed for simulated traverses including cases of flat, inclined, side slope, and sinusoidal terrain, with varying amounts of slip in the velocity analysis. The results showed good agreement with expected trends and values for the joint displacements and rates, with the largest percent deviation for the distance travelled being approximately 0.4 %. The results of the combined dynamic and terramechanics model, incorporating slip, are limited to the conceptual development of the model due to time constraints, and are thus inconclusive at this time. ii Dedication “Remember to look up at the stars and not down at your feet. Try to make sense of what you see and wonder about what makes the universe exist. Be curious. And however difficult life may seem, there is always something you can do and succeed at. It matters that you don't just give up.” Dr. Stephen Hawking iii Acknowledgements Foremost, the author would like to thank her primary supervisor Dr. M. J. D. Hayes for his valued guidance, advice, and overall support throughout the progression of this project, along with Dr. M. Faragalli for special advising. Special thanks are also due to Mission Control Space Services for providing a rover to model and their input regarding the Argo J5 rover. The author also wishes to express her deep gratitude to Dr. R. Irani for the use of his terramechanics model and for his coaching on the use of SimMechanics, and for his overall patience. Additional thanks go to the author’s friends and support group: her Grad School Survival Crew, fellow Shieldmaidens and kickboxing partners, A. Pant, G. Ng, J. Hunter, M. Magnus, and S. Milton, for their unwavering belief in the author’s capacity to achieve, while struggling through difficult times. Special thanks are due to G. Ng for allowing the author to bounce ideas off him. Finally, the author would like to thank her sister, parents, and four-legged family members for always having her back and providing encouragement to reignite her passion when it was needed the most. iv Table of Contents Abstract .............................................................................................................................. ii Dedication ......................................................................................................................... iii Acknowledgements .......................................................................................................... iv List of Figures ................................................................................................................... ix List of Tables .................................................................................................................. xiii Nomenclature ................................................................................................................. xiv Statement of Original Contributions ........................................................................... xix Chapter 1: Introduction .................................................................................................. 1 1.1 Martian Environment ...................................................................................................... 2 1.1.1 Obstacles ................................................................................................................ 4 1.1.2 Terrain Types ......................................................................................................... 7 1.2 Planetary Exploration Rovers ....................................................................................... 11 1.2.1 Rover Configurations ........................................................................................... 11 1.2.2 Argo J5 Rover ...................................................................................................... 13 1.3 Thesis Objectives and Outline ...................................................................................... 15 Chapter 2: Literature Review ....................................................................................... 18 2.1 Terramechanics and Wheel-Soil Interaction Models ................................................... 19 2.1.1 Empirical Methods ............................................................................................... 21 2.1.2 Analytical Methods .............................................................................................. 21 2.1.3 Semi-empirical Methods ...................................................................................... 25 2.2 Rover Vehicle Modeling .............................................................................................. 31 2.2.1 Kinematic Modeling ............................................................................................ 32 2.2.2 Dynamic Modeling .............................................................................................. 36 v 2.3 Slippage Estimation ...................................................................................................... 42 2.4 Performance Metrics .................................................................................................... 43 Chapter 3: Denavit-Hartenberg Methodology ............................................................ 45 3.1 Introduction to the Devanit-Hartenberg Convention .................................................... 46 3.2 D-H Procedure and Definition of Parameters ............................................................... 49 3.3 Homogeneous Transformation Matrices ...................................................................... 52 Chapter 4: Kinematic Analysis ..................................................................................... 55 4.1 Planar Kinematic Analysis – A Geometric Approach .................................................. 55 4.1.1 Theoretical Formulation ...................................................................................... 56 4.1.2 Method of Solution .............................................................................................. 63 4.1.3 Results .................................................................................................................. 66 4.2 Three-dimensional Position Kinematics (D-H Approach) ........................................... 72 4.2.1 Theoretical Formulation ...................................................................................... 72 4.2.2 Method of Solution .............................................................................................. 90 4.2.3 Results .................................................................................................................. 94 4.3 Three-dimensional Velocity Kinematics (D-H Approach) ......................................... 105 4.3.1 Theoretical Formulation .................................................................................... 105 4.3.2 Method of Solution ............................................................................................ 114 4.3.3 Results ................................................................................................................ 119 4.4 General Comments ..................................................................................................... 141 Chapter 5: Dynamic Analysis ..................................................................................... 144 5.1 Dynamic Model Development.................................................................................... 146 5.2 Terramechanics Model ............................................................................................... 151 5.3 Combined Dynamic and Terramechanics Model ....................................................... 156 5.4 Terramechanics Model Modifications ........................................................................ 164 vi 5.4.1 Preliminary Test Results for the Argo J5 Rover ................................................ 170 Chapter 6: Conclusions and
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