Safe control strategies for hopping over uneven terrain

Legged robots have long been proposed as a means of locomotion in unstructured environments. In recent years, researchers have developed small, robust, biologically inspired robotic systems that demonstrate an impressive ability to traverse diverse terrain and climb over obstacles at high speeds. However, much of the analysis to support this work has assumed level or slowly varying terrain. This dissertation explores the concept of safety as applied to hybrid dynamical systems as an analysis tool for legged robots in highly variable terrain. The robot must negotiate bound but unknown changes in terrain height between steps without stumbling or violating joint constraint limits. The problem is cast as a non-cooperative game where the robot attempts to maintain safe operation despite adversarial changes in the environment. The magnitude of the environmental disturbance that the robot can safely withstand is a measure of the system's "ruggedness" which is proposed as a possible design criterion. This thesis first considers a single legged vertical hopping robot with feedback control. Mechanical properties (stiffness and damping) which maximize ruggedness over variable terrain are identified. The thesis then considers timer based or open loop control of the vertical hopping robot. The addition of the timer state variable increases the dimensionality of the hopper problem from two states to three and requires a numerical tool for determination of the maximal invariant safe subset and least restrictive control. The development of this tool is a major topic of the dissertation. The tool is applicable to a broad but restricted class of hybrid systems. Results are given for a robot hopping vertically open loop over level ground, stairs, and variable terrain. Extension to planar running and multiple leg systems is discussed.