Characteristics of Spatial Human Arm Motion and the Kinematic Trajectory Tracking of Similar Serial Chains Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Satyajit S. Ambike, M.S. Graduate Program in Mechanical Engineering The Ohio State University 2011 Dissertation Committee: Dr. James P. Schmiedeler, Advisor Dr. Gary L. Kinzel, Co-advisor Dr. Robert A. Siston Dr. Richard J. Jagacinski Abstract This work studies spatial reaching motion in healthy humans. Research suggests that for individual instances of movement, the central nervous system (CNS) composes an ex- plicit wrist path, which is transformed into joint motions in a time-invariant fashion. This is the time invariance hypothesis (TIH), and its validation for spatial motion is the first goal of this study. The human arm is typically modeled as a multi-link, serial chain. When one joint of a serial chain is actuated, it simultaneously causes movement at other joints be- cause of interaction effects. Based on horizontal-plane reaching studies, the leading joint hypothesis (LJH) proposes that the interaction effects at (mostly) the proximal joint in the multi-link serial-chain model of the arm are low. Therefore, the CNS ignores this interac- tion effect to simplify the computation of joint torques and control of the joint trajectory. The second objective of this dissertation is to validate the LJH for spatial motion. In a spatial reaching experiment, healthy subjects performed point-to-point reaching movements at three distinct speeds. Data analysis revealed time-invariant wrist paths only for some subjects in some reaching tasks, suggesting that the TIH is not a truly general or- ganizing principle for spatial reaching motion. Therefore, this hypothesis needs refinement and further investigation. On the other hand, the interaction effects at the shoulder joint were small for a majority of the movements in this experiment so, the LJH was success- fully extended to spatial motion. i The TIH identifies the inputs and outputs of the first stage in the process of compos- ing the muscle activations for a given motor task. A computational algorithm that can potentially be used to execute this transformation was developed next. The algorithm, called speed-ratio control, also has beneficial applications in commercial robot control. It is demonstrated that the application of this algorithm to robotic serial chains provides greater navigational accuracy in the vicinity of certain kinds of singularities. Speed ratio control applies to non-redundant serial chains. The simplest model of the human arm consists of three-degree-of-freedom spherical joints at the shoulder and the wrist and a revolute joint at the elbow. This yields seven degrees of freedom for the arm. For positioning and orienting the hand relative to the thorax, only six degrees of freedom are necessary. The human arm is, therefore, a redundant serial chain. The formal process of extending the algorithm to redundant serial chains is undertaken. Initial work in which three- and four-degree-of-freedom planar chains track point paths is presented. Speed ra- tio control allows the resolution of the redundancy in the mechanism by maximizing the output-space tracking accuracy. Examples show superior local tracking performance with this approach compared to path tracking using unweighted pseudoinverse solutions. ii To my parents, Manik and Sanjeev. iii Acknowledgments I thank my advisor, Dr. J.P. Schmiedeler foremost for the opportunity he provided to me for doing this work. His support, patience, and guidance were key to the successful completion of this dissertation. I thank my committee members for providing insightful suggestions at various stages of this work. I thank my co-advisor, Dr. Kinzel for giving me opportunities to teach at the undergrad- uate and graduate level. This experience has helped me improve as a teacher enormously. I had many remarkably useful discussions with Dr. M. Srinivasan and Dr. A. Sheets. I thank you for your kindness. Similarly, I thank Dr. M.M. Stanisiˇ c´ at University of Notre Dame, who was instrumental in the development of some key ideas in this work. I thank the students from the University of Notre Dame for participating in my study. I also acknowledge the efforts of Julian Corona for helping me conduct these experiments. I get by with a little help from my friends, the Beatles sing. My journey for the past six years was rendered positively delightful by several people. Amongst them were Amod Damle, Satya Seetharaman, Sai and Sucheta Bhatwadekar, Janhavi Karandikar, Andrea Cordoba-Arenas, Arpit Mittal, Oren Costantini, Justin Persinger, Natalie Nazaryan, and Sachit Rao. You guys rock! Waroon, Abhijit and Sangeeta Varde deserve a special mention. The Vardes are my family, and the moral, psychological, and logistic support they have provided has been invaluable. iv Finally, I thank my parents. They have loved me without reservation. They have shown great patience toward me and faith in my abilities. I am fully aware that without these people and their support, the present work would not have been possible. v Vita June1999 ..................................B.E.,PuneUniversity July 1999-December 2001 . Design Engineer, Larsen & Toubro, Ltd June 2002 - December 2005 . Lecturer, Vishwakarma Institute of Tech- nology, Pune University January2006-March2007 .................. Graduate Teaching Assistant, The Ohio State University March2007 ................................Master of Science, The Ohio State Uni- versity April2008-March2009 .....................Graduate Research Assistant, Locomo- tion and Biomechanics Lab, The Ohio State University April 2009 - April 2010 . Presidential Fellow, The Ohio State Uni- versity May2010-October2010 ....................Graduate Teaching Assistant, The Ohio State University Research Publications 1. Ambike, S., Schmiedeler, J.P., & Stanisiˇ c,´ M.M., 2011, “Trajectory Tracking Via In- dependent Solutions to the Geometric and Temporal Tracking Subproblems”, ASME J. Mech. Robotics, vol. 3, no. 2, pp. 021008-1 - 021008-12. 2. Ambike, S., Schmiedeler, J.P., & Stanisiˇ c,´ M.,M., 2010, “Using Redundancy in Se- rial Planar Mechanisms to Improve Output-Space Tracking Accuracy,”, Advances in Robot Kinematics, Motion in Man and Machine, Ed. J. Lenarciˇ c,ˇ M. Stanisiˇ c,´ Springer. 3. Ambike, S., Schmiedeler, J.P., & Stanisiˇ c,´ M.,M., 2010, “Geometric, Spatial Path Tracking Using Non-Redundant Manipulators via Speed-Ratio Control,” Interna- tional Design Engineering Technical Conferences & Computers and Information in Engineering Conference, IDETC/CIE 2010, Montreal, Canada. vi 4. Ambike, S., & Schmiedeler, J.P., 2008, “Time-invariant strategies in coordination of human reaching,” Advances in Robot Kinematics: Analysis and Design, Ed. J. Lenar- ciˇ c,ˇ P. Wenger, Springer. 5. Ambike, S., & Schmiedeler, J.P., 2008, “A methodology for implementing the cur- vature theory approach to path tracking with planar robots”, Mech. Mach. Theory, vol. 43, no. 10, pp. 1225-1235. 6. Ambike, S., & Schmiedeler, J.P., 2007, “Application of geometric constraint pro- gramming to the kinematic design of three-point hitches”, Applied Engineering in Agriculture, vol. 23, no. 1, pp. 13-21. 7. Ambike, S., & Schmiedeler, J.P., 2007, “First-order coordination of the articulated arm subassembly using curvature theory”, Proceedings of the 2007 ASME Interna- tional Design Engineering Technical Conferences, Las Vegas. 8. Ambike, S., & Schmiedeler, J.P., 2006, “Modeling time invariance in human arm motion coordination,” On Advances in Robot Kinematics, Ed. J. Lenarciˇ c,ˇ B. Roth, Kluwer Academic Publishers. Fields of Study Major Field: Mechanical Engineering, Human Motor Control, Robot Kinematics and Dy- namics vii Table of Contents Page Abstract......................................... i Dedication........................................ iii Acknowledgments.................................... iv Vita ........................................... vi ListofTables ...................................... xi ListofFigures...................................... xiii ListofAbbreviations ................................ xx 1. Introduction.................................... 1 1.1 Humanmotorcontrol............................ 1 1.2 Humanarmmotion............................. 4 1.2.1 The time invariance hypothesis . 7 1.2.2 The leading joint hypothesis . 7 1.3 Kinematic trajectory tracking using serial chains . ......... 8 1.3.1 Singularity navigation with serial manipulators . ....... 10 1.3.2 Trajectory tracking with redundant, planar manipulators . 11 2. The kinematics of spatial human reaching . ...... 13 2.1 Introduction and background . 13 2.2 Experimentalmethods . 25 2.2.1 Dataanalysis............................ 32 2.3 Results ................................... 42 2.4 Discussion ................................. 66 2.5 Conclusions................................. 71 viii 3. The Dynamics of spatial human reaching: Investigating the Leading Joint Hy- pothesis....................................... 73 3.1 Introduction and background . 73 3.2 Equations of motion and torque partitioning for the humanarm ..... 76 3.3 Dataanalysis ................................ 94 3.4 Results ...................................100 3.5 Discussion .................................113 3.5.1 Relation between the TIH and the LJH . 117 3.6 Conclusions.................................121 4. Trajectory Tracking Via Independent