Feasibility of multiple robust control barrier functions for bounding box constraints

Enforcing multiple constraints based on the concept of control barrier functions (CBFs) is a remaining challenge because each of the CBFs requires a condition on the control inputs to be satisfied which may easily lead to infeasibility problems. The problem becomes even more challenging with input constraints and disturbances. In this paper, we consider enforcement of bounding box constraints for a second order system under limited control authority and input disturbances. To solve the constrained control problem, we apply multiple robust control barrier functions (RCBFs) which, in general, do not provide a feasible solution to the problem. However, we derive conditions on how to select the RCBF parameters to guarantee that a feasible solution always exists.