Robust Stabilization of Periodic Gaits for Quadrupedal Locomotion via QP-Based Virtual Constraint Controllers

Abstract

This letter develops, theoretically justifies, and experimentally implements an optimization-based nonlinear control methodology for stabilizing quadrupedal locomotion. This framework utilizes virtual constraints and control Lyapunov functions (CLFs) in the context of quadratic programs (QPs) to robustly stabilize periodic orbits for hybrid models of quadrupedal robots. Properties of the proposed QP are studied wherein sufficient conditions for the continuous differentiability of the controller are presented. Additionally, this letter addresses the robust stabilization problem of the orbits based on the Poincaré sections analysis and input-to-state stability (ISS). The proposed controller is numerically and experimentally validated on the A1 quadrupedal robot with 18 degrees of freedom to demonstrate the robust stability of trotting gaits against external disturbances and unknown payloads.

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