Almost driftless navigation of 3D limit-cycle walking bipeds

Abstract

This paper presents a method for navigating 3D dynamically walking bipedal robots amidst obstacles. Our framework relies on composing gait primitives corresponding to limit-cycle locomotion behaviors and it produces nominal motion plans that are compatible with the system's dynamics and can be tracked with high fidelity. The low-level controllers of the biped are designed within the Hybrid Zero Dynamics (HZD) framework. Exploiting the dimensional reduction afforded by HZD and properties of invariant sets of switching systems among multiple equilibria, we obtain polynomial approximations of a reduced order Poincaré map and of the net change of the center of mass location over a stride. These polynomials are then incorporated in a high-level Rapidly Exploring Random Tree (RRT) planner to generate nominal plans which are tracked by the biped with drastically low drifting errors, without adversely affecting the time for computation.