Safe Control Using High-Order Measurement Robust Control Barrier Functions

We study the problem of providing safety guarantees for dynamic systems of high relative degree in the presence of state measurement errors. To this end, we propose High-Order Measurement Robust Control Barrier Functions (HOMR-CBFs), an extension of the recently proposed Measurement Robust Control Barrier Functions. We begin by formally defining HO-MR-CBF, and identify conditions under which the proposed HO-MR-CBF can render the system's safe set forward invariant. In addition, we provide bounds on the state measurement errors for which the optimization problem for identifying the corresponding safe controllers is feasible for all states within the safe set and given restricted control inputs. We demonstrate the proposed approach through numerical experiments on a collision avoidance scenario in presence of measurement noise. We show that using our proposed control method, the robot, which has access to only biased state estimates, will be successful in avoiding the obstacle.