Passive dynamic walking with knees : a point foot model

In this thesis, a hybrid model for a passive 2D walker with knees and point feet is presented. The step cycle of the model has two phases of continuous dynamics: one with an unlocked knee configuration and a second one with a locked knee configuration. These stages are modeled as three-link and two-link pendulums correspondingly. The model switches between the two stages at knee-strike and heel-strike, which are both discrete events modeled as instantaneous inelastic collisions. The dynamics of this model were fully derived analytically. Furthermore, a stable gait was found given a set of physical parameters and initial conditions. A basic stability analysis of this stable limit cycle was performed around the fixed point of the Poincare return map examined right after heel-strike. This thesis also presents the design and construction of a planar robot based on this kneed walker model, as well as a careful examination of its correspondence to the motion predicted by the model simulation. The goal is to be able to study the nonlinear dynamics of simplified dynamic models which are also physically realizable, in order to build robots based on them in a more rigorous and reproducible manner. The work presented here aims to bridge the gap between existing theoretical models and successful experiments in passive dynamic walking. Thesis Supervisor: Russ Tedrake Title: Assistant Professor Acknowledgments Thanks to my advisor Russ Tedrake for offering his guidance and support throughout the project and in many other ways beyond the project itself, for sitting down with me to carefully go through specific concrete problems on many occasions, as well as for the many great abstract, ‘big-picture’ research conversations we had. I am most grateful for his passion and enthusiasm for robotics, which has inspired me and taught me to grow as a researcher and an engineer. I’d like to thank Stephen Proulx for designing and building the robot and for his excellent intuition for mechanical design which proved to be indispensable while we debugged the robot. Thanks for the countless hours of work on the robot, for helping me fix the little quirks and for fixing it the many times we crashed the robot entirely. Thanks also to Katie Byl, for the compass gait results and her insights and intuition with the project in general, and to Rick Cory for working through two classes together and the helpful comments about my research. To the entire lab, thanks for all the fun group meetings and jokes at the lab, and for being a source of energy and learning for me. I want to extend my thanks to my academic advisor, George Verghese, for his kindness and support and for giving me the liberty to pursue all my interests since I arrived at MIT, academic or non-academic. Thanks to my Physics advisor at Wellesley, Robbie Berg, for first introducing me to electronics and robotics. Also, thanks to Paula Echeverri, for persuading me to take that robotics class with her that first got me into robotics research. Most importantly, I am immeasurably grateful to family: to my parents for all their love and support which has helped me get to where I am today, and to my sisters, Mimian and Wen, for always being there for me.