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Jumping Behaviour for a Wheeled Quadruped Robot: Analysis and Experiments Jumping Behaviour for a Wheeled Quadruped Robot: Analysis and Experiments Adam Harmat Master of Engineering Department of Mechanical Engineering McGill University Montreal, Quebec 2008-10 A thesis submitted to McGill University in partial fulfillment of the requirements of the degree of Master of Engineering © Adam Harmat, 2008 ACKNOWLEDGEMENTS I would like to thank my supervisor Dr. Inna Sharf for her tremendous help throughout my degree program. Without her guidance and expertise, this work would not have been possible. I would also like to thank my parents, who have always completely supported all of my educational pursuits. I also wish to thank my lab mates at the Mechatronic Locomotion Laboratory, Michele Faragalli, Nicolas Plamondon, Chris Prahacs, Olivia Chiu, and David Cowan, for all their help and companionship over the past two years. Lastly, thanks are extended to Charles Steeves, Mike Tolley, and James Smith, all of whom authored significant work on PAW’s mobility which were referenced heavily. Funding for this research was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), and by Defence Research and Development Canada (DRDC). Thanks are given to Dr. Michael Trentini, project advisor at DRDC. ii ABSTRACT This thesis describes a new jumping behaviour developed for the quadruped robot PAW. The robot has very few degrees of freedom, employing springy legs and wheels at the distal ends of the legs to achieve its various modes of locomotion. This simple construction allows PAW to exploit the dynamics of a mass-spring system to achieve gaits such as bounding, galloping, and presently jumping. An MSC.ADAMS / Simulink co-simulation is used to develop and optimize the jumping process, which consists of four stages: acceleration to jumping speed, front hip thrusting, rear hip thrusting, and flight. Due to the strong coupling between the parameters describing the jump, manual tuning is not possible and thus a genetic algorithm is used for the optimization process. The data generated by the genetic algorithm is then used for the fitting of a quadratic response surface, which identifies those parameters that contribute most to a successful jump. The simulation is then generalized to allow robots of various geometries to be analyzed, and it is found that leg length and body length are important factors in the jumping behaviour. Finally, the possibility of extending this approach to simulate the jumping of virtually any wheeled-leg quadruped is discussed. iii SOMMAIRE Cette thèse décrit un nouveau comportement sautant développé pour le robot quadrupède PAW. Le robot a très peu de degrés de liberté, employant des ressorts dans les jambes et des roues aux bouts pour atteindre ses divers modes de locomotion. Cette construction simple permet à PAW d’exploiter la dynamique d'un système de masse-ressort pour atteindre l’allure du galop, du rebond, et le sujet de cette recherche: le saut. Une co- simulation de MSC.ADAMS et Simulink est utilisée pour développer et optimiser le processus sautant, qui consiste de quatre étapes : l'accélération pour atteindre la vitesse necessaire pour sauter, la poussée des jambes de devant, la poussée des jambes postérieur, et le vol. En raison du fort accouplement entre les paramètres décrivant le saut, l'accordement manuel de ces paramètres n'est pas possible. Alors, un algorithme génétique est utilisé pour le processus d'optimisation. Les données produites par l'algorithme génétique sont alors utilisées pour l’adjustement d'une surface de réponse quadratique, qui identifie les paramètres qui contribuent le plus à un saut réussi. La simulation est alors généralisée pour permettre aux robots de diverses géométries à être analysé, et il est trouvé que la longueur des jambes et la longueur du corps sont des facteurs importantes dans le comportement sautant. Enfin, la possibilité d'étendre cette approche pour simuler le saut de quasiment n'importe quel quadrupède avec des roues aux bouts des jambes est discuté. iv TABLE OF CONTENTS ACKNOWLEDGEMENTS................................................................................................ ii ABSTRACT....................................................................................................................... iii SOMMAIRE...................................................................................................................... iv LIST OF TABLES............................................................................................................ vii LIST OF FIGURES ......................................................................................................... viii Chapter 1. Introduction....................................................................................................... 1 1.1. Robot Locomotion ................................................................................................... 1 1.2. Quadruped Robots ................................................................................................... 5 1.3. Quadrupeds on Uneven Terrain............................................................................... 9 1.4. Background on PAW ............................................................................................. 12 1.5. Thesis Objectives................................................................................................... 14 Chapter 2. PAW Simulation Model.................................................................................. 16 2.1. Previous PAW Models........................................................................................... 16 2.2. Model Details......................................................................................................... 19 2.4. Simulation Improvements...................................................................................... 24 2.4.1. Electrical Model.............................................................................................. 25 2.4.2. Battery Model ................................................................................................. 25 2.4.3. Hip Amplifier and Motor Model..................................................................... 26 2.4.4. Wheel Amplifier and Motor Model ................................................................ 29 2.4.5. Hip Belt Model ............................................................................................... 31 2.5. Simulink Model ..................................................................................................... 36 2.6. Model Validation ................................................................................................... 38 Chapter 3. Jumping Behaviours on PAW......................................................................... 41 3.1. Steeves’ Behaviours............................................................................................... 41 3.2. Tolley’s Behaviours............................................................................................... 44 3.3. New Jumping Behaviour........................................................................................ 46 Chapter 4. Simple PAW Model and Dimensional Analysis............................................. 49 4.1. The Simple PAW Model........................................................................................ 49 4.2. Derivation of Equations of Motion........................................................................ 53 4.3. Validation............................................................................................................... 55 4.4. Non-Dimensionalized Model................................................................................. 58 4.5. Non-Dimensional Analysis.................................................................................... 62 v Chapter 5. Jump Implementation and Results .................................................................. 69 5.1. Key Jumping Parameters ....................................................................................... 69 5.2. Implementation on Physical PAW......................................................................... 77 5.3. Jump Optimization with Genetic Algorithm.......................................................... 81 5.4. Genetic Algorithm Results..................................................................................... 85 Chapter 6. Analysis of Optimization Results.................................................................... 88 6.1. Response Model Generation.................................................................................. 88 6.2. Physical Sensitivity Analysis................................................................................. 91 6.2.1. Video Analysis................................................................................................ 91 6.2.2. Physical Trials................................................................................................. 94 6.3. Generalized Optimization Model........................................................................... 98 Chapter 7. Conclusion..................................................................................................... 102 7.1. Summary of Work................................................................................................ 102 7.2. Future Work......................................................................................................... 104 7.2.1. Simulation Improvements............................................................................
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