A Topological Approach to Gait Generation for Biped Robots

This article describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2-D 3-D biped walkers subject configuration inequality constraints, physical holonomic constraints (e.g., linkages), virtual (user-defined enforced through feedback control). Our method constructs implicitly defined manifolds feasible periodic within state-time-control space that parameterizes the biped’s hybrid trajectories. Since equilibrium configurations often belong such manifolds, we use equilibria as “templates” from which grow gait families. Equilibria are reliable seeds construction families, eliminating need random, intuited, or bio-inspired initial guesses at trajectories in an optimization framework. We demonstrate on several walkers.