A Topological Approach to Gait Generation for Biped Robots

Nelson Rosa*, Kevin M. Lynch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This article describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2-D and 3-D 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 2-D and 3-D biped walkers.

Original languageEnglish (US)
Pages (from-to)699-718
Number of pages20
JournalIEEE Transactions on Robotics
Issue number2
StatePublished - Apr 1 2022


  • Humanoid and bipedal locomotion
  • legged robots
  • numerical continuation methods
  • underactuated robots

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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