Stable Control of a One Legged Robot Exploiting Passive Dynamics

To my wife, my daughter, and my parents. j j j j j j ii ABSTRACT ABSTRACT This thesis aims at the understanding, the design, the dynamics, and primarily, the control of a one{legged running robot with the goal of maximizing its energy eeciency. The approach exploits the leg's passive dynamics, the unforced periodic leg swing motion. We introduce a strategy, termed \Controlled Passive Dynamic Running," which tracks a varying desired forward speed in a stable and robust fashion, and at the same time enjoys high eeciency resulting from passive operation. A simpliied model of the running robot is used for preliminary studies. For this model, proper spring selection and initial conditions result in passive dynamic operation close to the desired running motion, without any actuation. However, this passive running is not stable and thus requires a stabilizing controller. The controller is based on online calculations of the desired passive motions, which are param-eterized in terms of a normalized \locomotion time." Simulation results show substantial reduction in the energy expenditure of the passive running robot compared to another robot without passive hip. A one-legged robot, \ARL Monopod II," is developed as a means for experimental validation of the control strategy. It features compliant elements in series with actuators at its hip and prismatic knee joint. Implementing the controller on the real robot results in a dramatic hip energy reduction of 60%, compared to an older robot without a passive h i p. As a result, the \speciic resistance" is reduced to 0:22 from the reported value of 0:7 for the older robot. The speciic resistance is used as a measure to compare several legged robots, other vehicles and human activities. A new controller for the vertical motion and its stability proof are provided. The dynamics of the robot is corrected by the controller to create a limit cycle similar to the one found by passive v ertical oscillations. A L y apunov-type function and Lasalle's theorems are used to prove that the resulting limit cycle is attractive and its domain of attraction is found explicitly. iii R ESUM E R ESUM E Cette th ese a pour but la compr ehension, la conception, la dynamique et, principalement, la commande d'un robot-coureur a une jambeavec l'objectif d'en maximiser le rendement energ etique. L'approche choisie exploite la dynamique passive d e l a j a m be, son balancement p eriodique libre. …