Abstract

In this paper, we present and verify methods for developing robust, high-level policies for metastable (i.e., rarely falling) rough-terrain robot walking. We focus on simultaneously addressing the important, real-world challenges of (1) use of a tractable mesh, to avoid the curse of dimensionality and (2) maintaining near-optimal performance that is robust to uncertainties. Toward our first goal, we present an improved meshing technique, which captures the step-to-step dynamics of robot walking as a discrete-time Markov chain with a small number of points. We keep our methods and analysis generic, and illustrate robustness by quantifying the stability of resulting control policies derived through our methods. To demonstrate our approach, we focus on the challenge of optimally switching among a finite set of low-level controllers for underactuated, rough-terrain walking. Via appropriate meshing techniques, we see that even terrain-blind switching between multiple controllers increases the stability of the robot, while lookahead (terrain information) makes this improvement dramatic. We deal with both noise on the lookahead information and on the state of the robot. These two robustness requirements are essential for our methods to be applicable to real high-DOF robots, which is the primary motivation of the authors.