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Towards Pronking with a Hexapod Robot Towards pronking with a hexapod robot Dave McMordie Department of Electrical Engineering McGill University, Montreal, Canada July, 2002 A thesis submitted to the Faculty of Graduate 5tudies and Research in partial fulfillment of the requirements of the degree Master of Engineering © Dave McMordie, 2002 National Library Bibliothèque nationale 1+1 of Canada du Canada Acquisitions and Acquisisitons et Bibliographie Services services bibliographiques 395 Wellington Street 395, rue Wellington Ottawa ON K1A DN4 Ottawa ON K1A DN4 Canada Canada Your file Votre référence ISBN: 0-612-85890-1 Our file Notre référence ISBN: 0-612-85890-1 The author has granted a non­ L'auteur a accordé une licence non exclusive licence allowing the exclusive permettant à la National Library of Canada to Bibliothèque nationale du Canada de reproduce, loan, distribute or sell reproduire, prêter, distribuer ou copies of this thesis in microform, vendre des copies de cette thèse sous paper or electronic formats. la forme de microfiche/film, de reproduction sur papier ou sur format électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts from it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou aturement reproduits sans son permission. autorisation. Canada Abstract RHex is a robotic hexapod with springy legs and just six actuated degrees of freedom. This work presents the development of a pronking gait for RHex, extending its efficiency and speed by exploiting its springy legs for hopping. A simple physical model of pronking is presented and verified qualitatively in simulation and experiment. In the course of analysing and attempting to stabilize pronking, the author develops an inertial attitude estimation system for RHex built around a three axis fibre-optic gyroscope. The author also validates a simple current estimation model for RHex's motors, which is then used to detect leg touchdown during pronking. II Résumé RHex est un robot à six pattes dont chaque jambe élastique est contrôlée par un seul moteur, placé a la hanche. Cette thèse décrit le dévelopment d'une nouvelle démarche pour RHex, le « pronk ». Cette démarche a permit une améloration de vitesse et éfficacité de locomotion de RHex, à cause de l'utilisation des jambes élastiques pour controller la motion verticale du centre de masse. En essayant de comprendre et de contrôler le « pronk », l'auteur a construit un nouveau système d'estimation d'orientation basé sur un gyroscope fibre-optique à trois axes. L'auteur a aussi verifié un modèle simple pour l'éstimation du courant dans un moteur qui est utilisé pour détecté l'atterisage du robot. III Acknowledgements Robotics research involves a huge amount of design, manufacturing, procurement and administration. Like ail aspects of the RHex project, this work was successful as much because of the hard work of the other members of the RHex team as because of my own efforts. l would especially like to thank those individuals whose contributions, technical or otherwise were essential to the author's work: • Martin Buehler (my advisor) for his guidance, ideas, criticism, support; for inventing RHex; and for fostering a strong sense of quality, team spirit and motivation in his lab. • Uluç Saranli for endowing RHex with its first physical incarnation and two generations of control software • Ben Brown and Edward Moore for designing the compliant four­ bar legs used for pronking. • Felix Grimminger for designing the half-circle legs which RHex has used over 50 much difficult terrain. • Don Campbell for designing RHex's 1/0 system, as weil as his numerous other technical and creative contributions • Matt Smith for his inspired and beautiful design of ail things mechanical on RHex • Haldun Komsuoglu for collaborating on numerous aspects of electronic design, and for many animated RHex discussions • Joel Weingarten showing us ail how much further RHex can go with a little learning. • Karen Coulter for her intrepid support of demos, software, hardware and administration for the RHex project. • Dan Koditshek for putting together and leading the RHex project; for guidance and support throughout this project. IV • Sarjoun Skaff for taking inertial sensing on RHex to a whole new level. • AI Rizzi for help with the gyro interface thread, as weil as many interesting discussions. • Prof. Robert J. Full for making the series of discoveries about animais which motivated the construction and study of RHex; for many valuable discussions. • Prof. Peter Caines for going the extra mile in helping me understand Kalman and Wiener filtering and how Kalman filtering may be applied to attitude estimation. • Team Northern Sun, McGill's Solar Vehicle Project for allowing me the opportunity to learn both team working and real-world design skills. • Guy-Anne Turgeon, Martin Cloake for the construction of T­ RHex, a low cost, scalable version of RHex. • The four horsemen, Jean E. Collin, Grand Smedley, Mathieu Bernier, Thomas Lavertu for the design and assembly of the shell version of RHex. • Danny Chouinard and Jan Binder for keeping CIM's computer facilities running, providing the tools and technologies we need to keep the lab going. • Mariene Gray and Cynthia Davidson for keeping CIM operational and properly caffeinated. • Genvieve Vinois for her invaluable administrative support, creativity and hard work in keeping the lab operational. • loannis Poulakakis, James Smith, Evgeni Kiriy and Carl Steeves for inspiring discussions about other ARL robots, and for their ideas about RHex. Thanks also to James for helping me v translate the abstract, and for a careful reading of the Attitude Estimation chapter. • My parents, Claire and Michael McMordie, for their love and support throughout this work, and for a close reading of several drafts. Finally, 1 wouId Iike to thank Heather Butler for her love, patience and support throughout this programme. It seemed to me that every time 1 got stuck on a problem Heather was there with both good ideas and encouragement. Thanks also to Heather for a careful last reading of this thesis. VI Contents CHAPTER 1 INTRODUCTION, BACKGROUND AND OVERVIEW 1 1.1 WHY WE BUllD lEGGED MACHINES 1 1.2 WHEElED AND TRACKED ROBOTS 1 1.3 HISTORY AND INSPIRATION OF RHEX 2 1.4 MOTIVATION FOR RUNNING GAITS 3 1.5 PRONKING? 6 1.6 RELEVANT WORK 8 Previous ARL Robots 8 Other robots 10 CHAPTER2 MOTOR MODELLING AND CURRENT ESTIMATION 11 2.1 BACKGROUND AND MOTIVATION 11 High performance control requires high performance sensing and actuation 11 2.2 A MOTOR 1DRIVE MODEl FOR OPEN Loop TORQUE CONTROL 12 Component Models and Assumptions 12 2.3 MOTOR MODEl VALIDATION 16 Sources oferror 17 Conclusions and Future Work 20 2.4 MOTOR DRIVE REDESIGN 21 The starting point 21 PWM drive topologies for OC motor control 23 The SA60 Module: a motor driver on a chip 25 PWM Drive Efficiency: Single ended vs Bipolar 26 Original Low-pass fi/ter design 27 Component Selection 28 Thermal support 30 MD v1.3 Driver Board Layout 34 VII 2.5 CONCLUSIONS AND FUTURE WORK 35 CHAPTER 3 AN ATTITUDE ESTIMATOR FOR RHEX 36 3.1 MOTIVATION 36 3.2 TECHNOLOGIES AVAILABLE 36 Ground-directed distance sensors 36 3.3 INERTIAL ATTITUDE ESTIMATION 38 Coriolis-effect gyro 39 Interferometrie Fibre-optic Gyros (iFOGs) 43 Technology Summary 44 3.4 THE KINEMATIC PROBLEM 47 Why three gyros are better than one 47 Selection ofcoordinate systems 48 Direction Cosine Kinematics and Integration 49 Quaternion Kinematics and Integration 51 3.5 SYSTEM OVERVIEW 53 3.6 GYRO NONLINEARITY CORRECTION 55 3.7 SYSTEM PERFORMANCE 57 3.8 FUTURE IMPROVEMENTS 58 CHAPTER 4 PRELIMINARY MaDEL AND CONTROL OF PRONKING 59 4.1 STANCE PHASE 59 4.2 FLIGHT PHASE 61 4.3 CONTROL TEMPLATE 61 4.4 MATERIALS AND TECHNOLOGIES REQUIRED 62 4.5 PRELIMINARY CONTROL 63 Touchdown detection state machine 63 Flight phase: leg retraction 64 Stance phase: Protraction 65 Combined control/er 66 4.6 EXPERIMENTAL RESULTS 67 Speed trials 67 VIII 4.7 TYPICAL LEG TRAJECTORY PLOT (TRIAL 2, LEG 1) 69 Model Validation 70 Multi-surface trials 73 4.8 DiSCUSSiON 74 Speed &Energetics 74 Summary ofexperimental results 75 4.9 SIMULATION OF BASIC PRONKING 76 Model Description 76 Model Parameters 76 Simulation results 77 Vertical dynamics 77 4.10 CONCLUSIONS AND PROJECTED IMPROVEMENTS 80 CHAPTER 5 PITCH CONTROL DURING PRONKING 82 5.1 INTRODUCTION AND MOTIVATION 82 5.2 INPUTS AND INTERACTIONS 82 5.3 Two HYPOTHESES FOR PITCH CONTROL 83 Kinematic Pitch control 83 Touchdown plane control 87 5.4 EXPERIMENTAL VALIDATION 89 5.5 DiSCUSSiON 93 CHAPTER 6 CONCLUSION AND FUTURE WORK 94 Top Layer 97 80ttom Layer 98 Heat sink 99 VG941-3D gyroscope interface-- schematic 100 VG941-3D gyroscope interface-- board layout 101 IX Figures Figure 1a,b: Packbot: a state of the art tracked-robot 1 Figure 2: Rhex 0: First version of the robot built by U. Saranli and M. Buehler 3 Figure 3: Desired leg angles versus time for RHex's tripod walk (based on figure from [3]) 4 Figure 4: Springbok pronking 6 Figure 5: Robots previously constructed at ARL. Clockwise from top left: Monopod 1, Monopod II, Scout 1, Scout II 9 Figure 6: Ciruit diagram for battery / amplifier / motor / gear combination 13 Figure 7: Detail of amplifier, output filter and motor 14 Figure 8: Validation of Motor Model During Walking 18 Figure 9: Validation of Motor Model During Pronking 18 Figure la: Improved fit using linear
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