Safety guarantee via periodic discrete-time high-order control barrier function: Application to bipedal robots

In this paper, the concept of periodic discrete-time high-order control barrier function (P-DHOCBF) is developed. The proposed P-DHOCBF is utilized to ensure the forward invariance of the safety set for discrete-time systems with periodic characteristics in system states of any relative degree. Focusing on the periodic forward walking problem of bipedal robots based on the variable-height inverted pendulum model, a periodic model predictive control optimization problem incorporating P-DHOCBF is formulated, and periodicity-related constraints are established. Compared to the existing discrete-time control barrier function, the proposed P-DHOCBF significantly reduces the conservatism of safety, thereby enhancing the system safety by promptly preventing unsafe occurrences. An illustrative example and simulation results based on a 12-degree-of-freedom (DOF) bipedal robot verify the effectiveness of the proposed approach.