Feasibility-guaranteed safety-critical control with high-order control barrier function method

The optimization of control systems under the presence of safety constraints and input constraints frequently involves the decomposition into a sequence of quadratic programs (QPs) facilitated by the utilization of high-order control barrier function (HOCBF). When the safety constraint conflicts with the input constraint, however, it leads to infeasibility within the QPs. In this article, a feasibility-guaranteed QP is proposed to tackle the challenge posed by the conflict between HOCBF constraint and input constraint. Firstly, the classical QP is added with a feasibility constraint which is derived from input constraint and HOCBF constraint, where the parameter of feasibility constraint is updated via a new QP obtained by control sharing property. Then, Type-2 HOCBF is investigated for the system with multiple HOCBF constraints, which effectively confines the system within a single HOCBF at the current time step. Finally, the efficacy of this approach is demonstrated through the application of obstacle avoidance in a 3-DOF robot system.