Robust safety-critical control design for robotic systems under input disturbances with multiple time-varying constraints

Robotic systems operating in dynamic environments are subject to diverse and complex safety requirements, whose enforcement becomes particularly challenging for control systems in the presence of input disturbances. To this end, this paper proposes a robust safety-critical control method based on control barrier functions (CBFs) to guarantee the satisfaction of multiple time-varying safety constraints for robotic systems subject to input disturbances, while also ensuring the feasibility of the associated CBF-based quadratic programme (QP) when input bounds are present. Multiple safety constraints are first synthesised into a single CBF candidate, which is used to construct a QP controller that yields the safe velocity in the kinematic layer, and a general method is proposed to ensure the feasibility of the CBF-QP under input bounds. A velocity tracking controller is then formulated as a QP based on an input-to-state stabilising control Lyapunov function (ISS-CLF), with a CBF constraint incorporated to limit the velocity tracking error. The resulting two-layer controller guarantees that the time-varying safety constraints are satisfied despite input disturbances. The proposed algorithm is validated through experiments on a 7-degree-of-freedom Franka Emika Panda robot.