# A Topological Approach to Gait Generation for Biped Robots

arXiv: https://arxiv.org/abs/2006.03785 · HTML: https://mlsanity.com/paper/2006.03785/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2020.

## Built on by (most cited first, 1 of 1)

- [Distortion-Resilient Robotic Imitation Learning for Autonomous Cable Routing](https://mlsanity.com/paper/2606.11577/) (2026)

## Abstract (arXiv)

This paper describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2D and 3D biped walkers subject to configuration inequality constraints, physical holonomic constraints (e.g.,closed-loop linkages), and virtual holonomic constraints (user-defined constraints enforced through feedback control). Our method constructs implicitly-defined manifolds of feasible periodic gaits within a state-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 at feasible trajectories in an optimization framework. We demonstrate the approach on several 2D and 3D biped walkers.