Stable, High-Force, Low-Impedance Robotic Actuators for Human-Interactive Machines by Stephen Paul Buerger S.M.M.E., Massachusetts Institute of Technology (2001) B.M.E., University of Dayton (1999) 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 2005 @ Massachusetts Institute of Technology 2005. All rights reserved. Author ....................... ......................... Department of Mechanical Engineering February 11, 2005 Certified by....... (/ Neville Hogan Professor Thesis Supervisor A ccepted by .............. ... ......................... Lallit Anand Chairman, Department Committee on Graduate Students MASSACHUSETTS INSTiTUTE OF TECHNOLOGY JAN 1 9 2006 LIBRARIES 2 Stable, High-Force, Low-Impedance Robotic Actuators for Human-Interactive Machines by Stephen Paul Buerger Submitted to the Department of Mechanical Engineering on February 11, 2005, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract Robots that engage in significant physical interaction with humans, such as robotic physical therapy aids, must exhibit desired mechanical endpoint impedance while simultaneously producing large forces. In most practical robot configurations, this requires actuators with high force-to-weight ratios and low intrinsic impedance. This thesis explores several approaches to improve the tradeoff between actuator force capacity, weight, and ability to produce desired impedance. Existing actuators that render impedance accurately generally have poor force densities while those with high force densities often have high intrinsic impedance. Aggressive force feedback can reduce apparent endpoint impedance, but compromises coupled stability. The common standard for ensuring coupled stability, passivity, can limit performance severely. An alternative measure of coupled stability is proposed that uses limited knowledge of environment dynamics (e.g. a human limb) and applies robust stability tools to port functions. Because of structural differences between interaction control and servo control, classical single-input, single-output control tools cannot be directly applied for design. Instead, a search method is used to select controller parameters for an assumed structure. Simulations and experiments show that this new approach can be used to design a force-feedback controller for a robot actuator that improves performance, reduces conservatism, and maintains coupled stability. Adding dynamics in series to change an actuator's physical behavior can also improve performance. The design tools developed for controller design are adapted to select parameters for physical series dynamics and the control system simultaneously. This design procedure is applied to both spring-damper and inertial series dynamics. Results show that both structures can be advantageous, and that the systematic design of hardware and control together can improve performance dramatically over prior work. A remote transmission design is proposed to reduce actuator weight directly. This design uses a stationary direct-drive electromagnetic actuator and a passive, flexible hydraulic transmission with low intrinsic impedance, thereby utilizing the impedance- 3 rendering capabilities of direct-drive actuation and the force density of hydraulic actuation. The design, construction and characterization of a low-weight, low-friction prototype for a human arm therapy robot are discussed. Recommendations and tradeoffs are presented. Thesis Supervisor: Neville Hogan Title: Professor 4 Acknowledgments Many stars had to align in order for me to complete this work, and this could only have happened with the assistance of a great many people who helped in small and large ways. A few are mentioned here, but thanks to all. First, last, and everywhere in between I thank Neville Hogan. Neville's ability to reduce a complex problem to its core questions is a huge part of his success and a skill that I have tried hard to learn. One talent that I will never match is his ability to recall long-dormant and seemingly unrelated information and apply it in detail to a new problem. Neville still doesn't realize that most of us can't do this. He has also developed great skill as an aerobatic pilot; most likely I will not even try to emulate this capability, but I am thrilled to enjoy the ride! I have also enjoyed many conversations and laughs with Neville throughout my time as his student. Professors David Trumper and David Hardt rounded out a superb committee; many thanks to them. Each has the rare combination of intuition for both phys- ical systems and applied control. Professor Trumper has developed some amazing technologies, and Professor Hardt's early work in fields related to my own proved a tremendous resource. It was humbling each time I gathered these three giants in a room, and my rate of learning was never higher than on these occasions. Many members of the Newman lab have been a great help through the years; I don't trust myself to recall a complete list, but a few people stand out. Jerry Palazzolo has a broad knowledge of mechanical engineering and controls, and has helped me with specific, firsthand insight in robust control, fluid power, and many other areas. Brandon Rohrer always patiently humored my questions and was an excellent sounding board for my technical ideas, and he has continued to provide advice and encouragement from afar. Igo Krebs's experience with getting hardware built and projects done was always a great help. Sue Fasoli's perspective as a clinician has dramatically improved the quality of the group's engineering by helping us to better understand the practical issues. Steven Charles and Josh Young are admirably continuing the Hogan lab presence on the south mezzanine. Laura, Sarah, Shelly, Nevan, and Ryan continue to churn out fascinating and useful work. Marj Joss does a fantastic job of making everything run smoothly. Thanks to all of them and to everyone else who has worked in the research group. Bryan Crane has navigated grad school in parallel with me, and I thank him for his company and encouragement through the roller coaster. Max Berniker brings a unique perspective to everything from two-norms to television production, and I am sure he will feel vindicated when humanity drains its last drop of oil from beneath the Caspian Sea. Patrick Anquetil is a wellspring of positivity (though I still think he started the fire at our former household). Thanks to Matt Spenko (& Elizabeth), Robert David, Ben Paxton, Matt Lichter, Justin Verdirame, and all my other MIT friends. 5 Connections to friends outside of MIT have always been essential for me. Mike Burrows always reminds me of the importance of carefree days. Kirk Vashaw is a great friend and counterpart for heated political debates. No one is quicker to seize the opportunity to go out than Kevin O'Neill (who was never really an MIT guy). I also especially thank all the other Boston people, including Theresa & crew, Matt Cole, and all of Nicole's friends. People from elsewhere provided essential support and the chance to escape, whether on the phone or in person. Thanks to Patrick King, Patrick Schubel, Rob O'Leary, Matt Groves, Jill & Rob, Guapo, Casey, Chris Luckett, Purcell, Paul Haney, and many others, including my entire extended family on both sides. I give a great big thanks to my parents for listening to my constant complaints and for continually assuring me that everything would work out in the end. I am sure they are glad this phase is over. Thanks to my sister Julia, her husband John and especially my two nieces, Emily and Rebecca, for reminding me that there are many more important things in life than grad school (for example, being sure that your noodles get exactly the right amount of sauce on top: none). And finally I thank Nicole. No one has had a more unfiltered view of the challenges I've faced over the past few years and my reactions to them, and she has stood firm in the face of all my flaws longer than I ever could have hoped. Her caring smile has brought joy to the bleakest days. For that I owe her everything. Thank you Nicole. This work was supported by a National Defense Science and Engineering Graduate Fellowship, by the Burke Medical Research Institute, by National Institutes of Health grant #RO1-HD37397, and by the Spinal Cord Injury Board of New York State. 6 Contents 1 Introduction to the Interaction Problem 27 1.1 Defining Mechanical Interaction . . . . . . . . 31 1.1.1 Signal and limited physical interaction . . . . . . . . . . . . . 32 1.2 Devices that Interact with Humans ............. ...... 3 3 1.2.1 Restrictive devices . . . ............ ....... 3 3 1.2.2 Low-force active devices ............ ....... 3 4 1.2.3 High-force active devices ............ ....... 3 4 1.3 Low Mechanical Impedance . . ........... ........ 3 5 1.4 Evaluating Interactive Robots . ......... .......... 3 7 1.4.1 Stability . . . . . . . . . ........ ... ........ 3 7 1.4.2 Performance . . . . . . . ........ .. ......... 3 8 1.4.3 Other factors . . . . . . ...... ............. 3 8 1.5 Evaluating Actuators . . . . . . ................... 3 8 1.6 Actuator for Robotic Therapy . ................... 3 9 1.7 Thesis organization . . . . . . . ................... 4 2 2 State of the Art in Interactive Machines 45 2.1 Quantifying actuator and haptic device performance . 45 2.2 Existing actuation technologies . . . . . . . . . . . . 47 2.2.1 Direct-drive electromagnetic actuation . . . . 47 2.2.2 Electromagnetic actuators with gears . . . . . 53 2.2.3 Electromagnetic actuators with remote transmissions . . . 59 2.2.4 H ydraulics . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 7 2.2.5 Pneum atics . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 2.2.6 Interactive actuator design space . . . . . . . . . . . . . . . 66 2.3 Control for interactive applications . . . . . . . . . . . . . . . . . . 68 2.3.1 Effect of interaction on performance and stability . . . . . . 68 2.3.2 Interaction as disturbance rejection or modeling uncertainty 73 2.3.3 Regulating dynamic behavior . . . . . . . . . . . . . . . . . 74 2.3.4 Analyzing coupled systems . . . . . . . . . . . . . . . . . . . 78 2.3.5 Implementing interaction control . . . . . . . . . . . . . . . 87 2.3.6 Improving low-impedance performance . . . . . . . . . . . . 91 3 Design of Controllers Using Limited Knowledge of the Environment 105 3.1 Passive control and human-robot interaction . . . . . . . . . . . . . . 106 3.1.1 Passivity as too conservative for human limb interaction . . . 106 3.1.2 Passivity as insufficient for coupled stability . . . . . . . . . . 107 3.2 Non-passive robots in practice . . . . . . . . . . . . . . . . . . . . . . 108 3.3 Classical control design with model of environment . . . . . . . . . . 109 3.3.1 Servo control and interaction control . . . . . . . . . . . . . . 110 3.4 Interaction control design as optimization constrained to robust stability118 3.4.1 Evaluating stability . . . . . . . . . . . . . . . . . . . . . . . . 119 3.4.2 Measuring performance . . . . . . . . . . . . . . . . . . . . . . 124 3.5 Algorithm structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4 Control Algorithm Validation 131 4.1 Details of example . . . . . . . . . . . . . . . . . . . . . . . . 131 4.1.1 Robot model . . . . . . . . . . . . . . . . . . . . . . . 131 4.1.2 Environment model . . . . . . . . . . . . . . . . . . . . 134 4.1.3 Cost function and target impedance . . . . . . . . . . . 137 4.1.4 Controller form and robot port impedance . . . . . . . 138 4.2 Com putation . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 4.2.1 Numeric issues . . . . . . . . . . . . . . . . . . . . . . 144 4.2.2 Computational Load . . . . . . . . . . . . . . . . . . . 149 8 4.3 Initial algorithm results . . . . . . . . . . . . . . . . . . . . . . 150 4.3.1 Proportional gain . . . . . . . . . . . . . . . . . . . . . 150 4.3.2 Single-zero (PD) control . . . . . . . . . . . . . . . . . 152 4.3.3 Single-pole (lowpass) control . . . . . . . . . . . . . . . 153 4.3.4 Lead and lag controllers . . . . . . . . . . . . . . . . . 154 4.3.5 Results analysis . . . . . . . . . . . . . . . . . . . . . . 156 4.3.6 Nonzero target impedance . . . . . . . . . . . . . . . . 164 4.3.7 Natural admittance control . . . . . . . . . . . . . . . 170 4.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 174 4.4.1 Coupled stability testing . . . . . . . . . . . . . . . . . 175 4.4.2 Comparison of model and experiment . . . . . . . . . . 184 4.4.3 Performance testing . . . . . . . . . . . . . . . . . . . . 190 4.4.4 Conclusions from initial results . . . . . . . . . . . . . 197 5 Series Dynamics to Improve Interaction 199 5.1 Benefits of series dynamics . . . . . . . . . . . . . . . . . . . . . . . 200 5.1.1 Changing physical system structure . . . . . . . . . . . . . . 201 5.1.2 Stabilizing force-feedback systems . . . . . . . . . . . . . . . 204 5.1.3 Design strategies for series dynamics . . . . . . . . . . . . . 205 5.2 Integrated design of series dynamics and control . . . . . . . . . . . 211 5.2.1 Applying search method . . . . . . . . . . . . . . . . . . . . 212 5.2.2 Purely mechanical benefits . . . . . . . . . . . . . . . . . . . 212 5.2.3 Mechanical filters for passivity with fixed nonpassive control 214 5.2.4 Complementary stability and fixed nonpassive control . . . . 218 5.2.5 Variable control with series dynamics . . . . . . . . . . . . . 219 5.2.6 Multiple operating conditions . . . . . . . . . . . . . . . . . 224 5.2.7 Alternative parameter variation . . . . . . . . . . . . . . . . 229 5.2.8 Inertial series dynamics . . . . . . . . . . . . . . . . . . . . . 230 5.3 Series dynamic conclusions . . . . . . . . . . . . . . . . . . . . . . . 233 9 6 Remote Transmission for Actuator Weight Reduction 235 6.1 Hydraulic transmissions with electromagnetic actuators . . . . . . . 236 6.2 Requirements for two series fluid architectures . . . . . . . . . . . . . 237 6.2.1 Low source impedance, transparent transmission . . . . . . . 237 6.2.2 High source impedance, dominant fluid dynamics . . . . . . . 238 6.3 Design of mechanically transparent fluid transmissions . . . . . . . 240 6.3.1 Linear travel configuration . . . . . . . . . . . . . . . . . . . . 240 6.3.2 Differences from servo-hydraulics . . . . . . . . 243 6.3.3 Advantages . . . . . . . . . . . . . . . . . . . . 243 6.3.4 Tensile force transmission . . . . . . . . . . . . 246 6.3.5 Fluid dynamics . . . . . . . . . . . . . . . . . . 251 6.3.6 Line compliance . . . . . . . . . . . . . . . . . . 262 6.3.7 Design tradeoffs . . . . . . . . . . . . . . . . . . 264 7 Fluid Transmission Design Example and VTalidatio 1 267 7.1 Specifications and goals . . . . . . . . . . . . . . . . . . . . . 267 7.2 Prototype design . . . . . . . . . . . . . . . . . . . . . . . . 269 7.2.1 Source actuator . . . . . . . . . . . . . . . . . . . . . 269 7.2.2 Piston-cylinder and moving seals . . . . . . . . . . 269 7.2.3 Hydraulic fluids . . . . . . . . . . . . . . . . . . . . . 276 7.2.4 Fittings and static seals . . . . . . . . . . . . . . . . 277 7.2.5 Bias pressure mechanism . . . . . . . . . . . . . . . . 280 7.2.6 Fluid mechanics and hose selection . . . . . . . . . . 281 7.2.7 Linear bearing and structure . . . . . . . . . . . . . . 288 7.2.8 Leakage and fluid makeup . . . . . . . . . . . . . . . 291 7.3 Testing and characterization . . . . . . . . . . . . . . . . . . 292 7.3.1 Weight of outer assembly . . . . . . . . . . . . . . . . 293 7.3.2 Force capacity . . . . . . . . . . . . . . . . . . . . . . 295 7.3.3 Leakage and makeup . . . . . . . . . . . . . . . . . . 296 7.3.4 Virtual stiffness and stiffness measurement . 298 10