Robust Adaptive Control Barrier Functions for Input-Affine Systems: Application to Uncertain Manipulator Safety Constraints

Most existing control barrier functions-based control strategies for manipulator systems require a perfect knowledge of the model or consider the worst-case uncertainties. To solve this problem, a composite learning-enhanced adaptive optimal control approach is first proposed for manipulator systems, which achieves constraint satisfactions of joint positions and velocities in the presence of model uncertainties, and leveraging historical data online reduces uncertainties in estimated parameters. Technically, to ensure constraint satisfactions, a series of zeroing control barrier functions are designed, based on which the conditions that guarantee the forward invariance of the constraint-admissible set are derived. Then, a data-driven approach is utilized to reduce the conservatism of the robust adaptive control barrier functions by tightening the bounds of the unknown parameters. A manipulator system illustrates the effectiveness of the proposed method.