Fast and Strong Lightweight Robots based on Variable Gear Ratio Actuators and Control Algorithms Leveraging the Natural Dynamics by Alexandre Girard B.Ing., Université de Sherbrooke (2010) M.Sc.A., Université de Sherbrooke (2013) Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2017 ○c Massachusetts Institute of Technology 2017. All rights reserved. Author ................................................................ Department of Mechanical Engineering March 31th, 2017 Certified by............................................................ H. Harry Asada Ford Professor of Engineering Thesis Supervisor Accepted by ........................................................... Rohan Abeyaratne Chairman, Department Committee on Graduate Theses 2 Fast and Strong Lightweight Robots based on Variable Gear Ratio Actuators and Control Algorithms Leveraging the Natural Dynamics by Alexandre Girard Submitted to the Department of Mechanical Engineering on March 31th, 2017, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract In many applications, robots have to bear large loads while moving slowly and also have to move quickly through the air with almost no load. These type of bi- modal tasks, with conflicting requirements in terms of operating speeds and desired impedances, often lead to the use of oversized and inefficient actuators which are inhibitory particularly for mobile robots. Multiple gear ratios, like in a powertrain, address this issue by allowing an effective use of power over a wide range of output speeds, by enabling significant changes to the reflected intrinsic actuator impedances and by making possible the leveraging or attenuation of the natural load dynam- ics. This thesis aims to develop the technological solutions needed to use variable gear ratio actuators and exploit the advantages of variable transmissions in a robotic context. First, by addressing the issue of how to make fast and seamless gearshifts between two very different reduction ratios under diverse load conditions, with a so- lution based on a dual-motor actuator architecture and a control scheme using the null space. Second, by developing control algorithms that select optimal gear ratios dynamically based on state feedback, to move with minimal motor torques and to adjust the output impedance appropriately given a task. The proposed approach exploit variable transmissions not merely for increasing maximum torque and speed, but also to significantly alter the dynamic properties, including load sensitivity, ro- bustness, and backdrivability. Simulations and experiments using a novel lightweight robotic arm using three custom-built dual-speed dual-motor actuators are presented. Results demonstrate very fast gear shifting in highly dynamic situations with dual- speed dual-motor actuators, and show that actively changing gear ratios using the proposed control algorithms can lead to an order-of-magnitude reduction of necessary motor torque and power. Thesis Supervisor: H. Harry Asada Title: Ford Professor of Engineering 3 4 Acknowledgments I would first like to thank my thesis advisor, Professor Asada, who gave me the opportunity to work on unique robotic research projects in the d’Arbeloff laboratory. His guidance was invaluable, always thinking ahead to guide my efforts in a direction that would generate innovative and relevant research. I hope that I have learned some of his wisdom during my years at MIT. Also, special thanks to Professor Hogan and Professor Slotine for been members of my thesis committee: Their advices and feedback contributed to strengthening my thesis. Many thanks to all my labmates at the d’Arbeloff laboratory. The lab was a very dynamic and exciting place to work. Special mention to Lluis and Kosuke for spending precious time helping me reviewing technical drawings of gearbox prototypes. I would also like to thank the whole MIT community, for being a constant source of inspiration. The education I have received during my PhD studies was of outstanding quality, and I learned a lot spending time with members of the MechE and the CSAIL community. I would also like to thank The Boeing Company, Sumitomo Heavy Industry, Le Fond Québécois de Recherche sur la Nature et Technologie (FQRNT)andTheNatural Sciences and Engineering Research Council of Canada (NSERC), who contributed to funding my PhD studies at MIT. I must also acknowledge the strong support I have received from my friends and family. My wife Catherine has given outstanding support, and I could not have accomplished everything I did without her. I must also thank all my friends who came to visit me in Boston; their visits provided me with breaks from the frenetic lifestyle of MIT studies. I would also like to thanks my parents for always encouraging me in my studies, and Jean-Sébastien for giving me the push I needed to pursue my ambitions. Without them I would never have been able to pursue my dream at MIT. 5 6 Contents 1 Introduction 19 1.1 Proposed approach: variable transmissions . . . . . . . . . . . . . . . 20 1.1.1 Features of gear shifting in a robotic context . . . . . . . . . . 21 1.1.2 Differences from vehicle powertrain transmissions . . . . . . . 22 1.2 Main challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.3 Original contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.3.1 A gear shifting methodology adapted to robotics . . . . . . . . 25 1.3.2 Control algorithms to select gear ratios dynamically . . . . . . 25 1.3.3 A robotic arm using variable gear ratio actuators . . . . . . . 25 1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.5 Organization of the thesis . . . . . . . . . . . . . . . . . . . . . . . . 27 2 Aircraft Manufacturing Automation: Concepts and Challenges 29 2.1 Current situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2 Solution concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.2.1 Lightweight long manipulator arms . . . . . . . . . . . . . . . 30 2.2.2 Wearable robots . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.2.3 Mobile climbing robots . . . . . . . . . . . . . . . . . . . . . . 32 2.3 Technical challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3 A Variable Gear-ratio Actuator with Fast and Seamless Transitions 35 3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.2 Actuator and powertrain research . . . . . . . . . . . . . . . . . . . . 37 7 3.2.1 Novel contribution . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2.2 Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3 Dual-Speed Dual-Motor architecture . . . . . . . . . . . . . . . . . . 46 3.3.1 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.3.2 Weight advantage . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.3.3 Efficiency advantage . . . . . . . . . . . . . . . . . . . . . . . 50 3.3.4 Reliability advantage . . . . . . . . . . . . . . . . . . . . . . . 51 3.4 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.4.1 3-ports planetary gear junction . . . . . . . . . . . . . . . . . 52 3.4.2 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.4.3 Inputs/Outputs equations . . . . . . . . . . . . . . . . . . . . 56 3.4.4 Hybrid Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.4.5 Continuous differential equations . . . . . . . . . . . . . . . . 59 3.4.6 Gear-shift events . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.4.7 Output Impacts . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.4.8 Nullspace of the system during high-speed mode . . . . . . . . 62 3.4.9 Equivalence to a two-speed transmission . . . . . . . . . . . . 63 3.5 Control algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.5.1 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.5.2 State-machine . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.5.3 High-force mode controller . . . . . . . . . . . . . . . . . . . . 66 3.5.4 High-speed mode controller . . . . . . . . . . . . . . . . . . . 66 3.5.5 Fast and seamless transitions (gearshifts) . . . . . . . . . . . . 66 3.5.6 Synchronization controller . . . . . . . . . . . . . . . . . . . . 68 3.5.7 Preparation in the nullspace for faster down-shifts . . . . . . . 70 3.6 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.6.1 DSDM dynamic behavior . . . . . . . . . . . . . . . . . . . . . 74 3.6.2 Nullspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.6.3 Seamless transitions . . . . . . . . . . . . . . . . . . . . . . . 77 3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 8 3.8 Potential directions of further development . . . . . . . . . . . . . . . 82 4 Optimal Dynamic Selection of Gear-ratios 83 4.0.1 Illustration of the principle for a 1-DoF manipulator . . . . . . 84 4.0.2 Challenges and related works . . . . . . . . . . . . . . . . . . 85 4.0.3 Original contributions . . . . . . . . . . . . . . . . . . . . . . 88 4.1 Control architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.2 Modeling variable gear-ratio actuators . . . . . . . . . . . . . . . . . 91 4.2.1 1-DoF system . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.2.2 Generalization to n-DoF manipulators . . . . . . . . . . . . . 91 4.2.3 Limitation of the simplified model . . . . . . . . . . . . . . . . 93 4.2.4 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.2.5 Hybridness with discrete gear-ratios . . . . . . . . . . . . . . . 94 4.3 Optimal gear-ratios along a trajectory . . . . . . . . . . . . . . . . . 96 4.3.1 Selection criteria . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.3.2 Optimization Formulation . . . . . . . . . . . . . . . . . . . . 97 4.3.3 Minimal Torque Solution . . . . . . . . . . . . . . . . . . . . . 97 4.3.4 Reduction to impedance matching . . . . . . . . . . . . . . . . 98 4.3.5 Examples of optimal gear-ratios in simple scenarios . . . . . . 99 4.4 Model-based Controllers . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.4.1 R* Computed Torque . . . . . . . . . . . . . . . . . . . . . . . 100 4.4.2 R* Sliding Mode Control . . . . . . . . . . . . . . . . . . . . . 102 4.4.3 Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.4.4 Generalization to more complex models . . . . . . . . . . . . . 106 4.4.5 Closed-loop selection of discrete gear-ratios . . . . . . . . . . . 106 4.4.6 Rollout gear-ratios selection . . . . . . . . . . . . . . . . . . . 108 4.4.7 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.4.8 Chattering and high-frequency switching . . . . . . . . . . . . 112 4.4.9 Parameters selection guidelines . . . . . . . . . . . . . . . . . 115 4.5 Trajectory planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 9 4.5.1 RRT algorithm for Robots with Discrete Gear-ratios . . . . . 118 4.6 Dynamic programming approach . . . . . . . . . . . . . . . . . . . . 120 4.6.1 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . 120 4.6.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.6.3 Cost function . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.6.4 Value Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.6.5 Example systems . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.6.6 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4.6.7 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . 124 4.6.8 Advanced dynamic programming techniques . . . . . . . . . . 129 4.7 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 4.7.1 Model-based approach . . . . . . . . . . . . . . . . . . . . . . 130 4.7.2 Comparison to fixed-gear performance . . . . . . . . . . . . . 132 4.7.3 Comparison to Value Iteration . . . . . . . . . . . . . . . . . . 133 4.7.4 Fast gear-shifting inhibition . . . . . . . . . . . . . . . . . . . 134 4.8 Experiments Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 4.8.1 R* Computed Torque controller and RRT trajectory . . . . . 135 4.8.2 R* Sliding Mode controller . . . . . . . . . . . . . . . . . . . . 137 4.8.3 2-DoF experiments . . . . . . . . . . . . . . . . . . . . . . . . 138 4.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 4.10 Potential directions of further development . . . . . . . . . . . . . . . 140 5 The DSDM Lightweight Arm 141 5.1 Mechanical Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 5.1.1 DSDM actuator design . . . . . . . . . . . . . . . . . . . . . . 143 5.1.2 Arm design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 5.1.3 Limitations and recommendations for improvements . . . . . . 153 5.2 Control and Software Architecture . . . . . . . . . . . . . . . . . . . . 154 5.2.1 Global architecture . . . . . . . . . . . . . . . . . . . . . . . . 154 5.2.2 ROS architecture . . . . . . . . . . . . . . . . . . . . . . . . . 155 10