Gait Dynamics Evolution of a Passive Walking Robot with Asymmetric Leg Length and Arcuate Feet

This study explores the effects of leg asymmetry on gait dynamics in passive walking robots by proposing the normalized leg length deviation ratio as a fundamental parameter to assess inter-leg structural variations. Based on Lagrangian dynamics, an asymmetric compass model was established, and methods including Poincaré mapping, bifurcation theory, and Lyapunov exponents were employed to systematically investigate periodic gaits and bifurcation characteristics under the coupled effects of leg length deviation ratio and slope inclination. The study reveals that synergistic variations in asymmetric leg length and slope inclination significantly influence the system's bifurcation characteristics, not only inducing period-doubling bifurcation but also leading to fold bifurcation paths. This research elucidates the impact mechanism of synergistic variations in leg structure asymmetry and slope inclination on the gait dynamics of robotic systems. The findings provide theoretical insights for structural optimization of bipedal robots and enhancement of environmental adaptability in passive walking robots.