A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics

2025/08/30 by Esteban, Sergio A., Cohen, Max H., Ghansah, Adrian B. +1
#FOS: Computer and information sciences #FOS: Electrical engineering #Robotics (cs.RO) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2509.00294

Abstract

Reduced-order models (ROMs) provide a powerful means of synthesizing dynamic walking gaits on legged robots. Yet this approach lacks the formal guarantees enjoyed by methods that utilize the full-order model (FOM) for gait synthesis, e.g., hybrid zero dynamics. This paper aims to unify these approaches through a layered control perspective. In particular, we establish conditions on when a ROM of locomotion yields stable walking on the full-order hybrid dynamics. To achieve this result, given an ROM we synthesize a zero dynamics manifold encoding the behavior of the ROM -- controllers can be synthesized that drive the FOM to this surface, yielding hybrid zero dynamics. We prove that a stable periodic orbit in the ROM implies an input-to-state stable periodic orbit of the FOM's hybrid zero dynamics, and hence the FOM dynamics. This result is demonstrated in simulation on a linear inverted pendulum ROM and a 5-link planar walking FOM.

Citations

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• Formal Connections between Template and Anchor Models via Approximate Simulation
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Related

• Beyond Inverted Pendulums: Task-optimal Simple Models of Legged Locomotion
• Optimal Reduced-order Modeling of Bipedal Locomotion
• Learning Spring Mass Locomotion: Guiding Policies with a Reduced-Order\n Model
• DRS-LIP: Linear Inverted Pendulum Model for Legged Locomotion on Dynamic Rigid Surfaces
• Robust Push Recovery on Bipedal Robots: Leveraging Multi-Domain Hybrid Systems with Reduced-Order Model Predictive Control