Computation of Regions of Attraction for Hybrid Limit Cycles Using Reachability: An Application to Walking Robots

Contact-rich robotic systems, such as legged robots and manipulators, are often represented hybrid systems. However, the stability analysis region-of-attraction computation for these systems challenging because of discontinuous state changes upon contact (also referred to state resets ). In this work, we cast a Hamilton-Jacobi (HJ) reachability problem. This enables us leverage HJ tools that compatible with general nonlinear system dynamics, can formally deal input constraints well bounded disturbances. Our main contribution is generalization framework account originating from resets, which has remained challenge until now. We apply our approach computing region-of-attractions several underactuated walking demonstrate proposed (a) recover bigger than state-of-the-art approaches, (b) handle external disturbances, constraints, (c) also provides stabilizing controller resets enhancing stability.