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

A Topological Approach to Gait Generation for Biped Robots