Control of Biped Sideways Walking with Two-Periodic Gait Design

This paper presents a Hybrid Zero Dynamics (HZD) based control approach to achieve sideways walking for underactuated bipedal robots. As sideways walking involves no knee flexion and very small ankle pronation-supination, a two-link compass gait model can well represent the dynamics during sideways walking. Unlike forward walking (or sagittal-plane walking), which typically exhibits a 1-periodic gait (or walking orbit) due to leg symmetry, sideways walking demonstrates a 2-periodic gait consisting of two steps, the extending and contracting steps within one stride. This paper presents the invariance condition for constructing a 2-periodic gait and derives the computational results that can enforce this invariance condition. Moreover, the boundary conditions are derived for a given 2-periodic gait. Preliminary simulation on a feasible gait suggests that the controller is stable in terms of tracking the desired gait and can reject some disturbance.