Control of walking gaits in a bipedal robot with impulsive actuation

Abstract The period- $1$ gait is a stable, efficient, and predictable walking pattern for bipedal robots, which is crucial for achieving precise control, energy optimization, and maintaining balance in complex environments. This study investigates the control of chaotic and multi-period gaits in a bipedal robot with impulsive actuation, focusing on the stabilization of such gaits into period-1 gaits and the expansion of their stable parameter regions. Three main contributions are presented: (1) stabilizing chaotic gaits to period- $1$ gaits using the Ott–Grebogi–Yorke (OGY) and bifurcation control methods; (2) converting multi-period gaits (e.g., period- $2$ and period- $4$ ) into period- $1$ gaits via bifurcation control; and (3) extending the stable parameter range of period- $1$ gaits by optimizing pulse thrust parameters. The bifurcation control method, though energy-intensive, proves more reliable than OGY method in preventing falls. Analytical and numerical results demonstrate that adjusting pulse thrust parameter $C$ significantly expands the stability domain, enhancing robustness against disturbances and parameter variations. The bifurcation control method proposed in this study is implemented via a constant thrust increment and validated through numerical simulations, which makes it easy to be applied in controller design. It provides both a theoretical foundation and a practical control scheme for achieving stable and efficient gait design in bipedal robots with impulsive actuation.