A Backup Control Barrier Function Approach for Safety-Critical Control of Mechanical Systems Under Multiple Constraints

Ensuring multiple constraints, including time-varying state, time-invariant state, and input constraints, is crucial for the safe operation of robotic systems. A control barrier function-based quadratic programming (CBF-QP) safety filter offers a promising solution but can easily become infeasible, potentially leading to violations or requiring a fallback strategy. This article introduces a feasibility-guaranteed safety filter based on a backup CBF approach. First, rectified backup CBF-QP is introduced with a common backup policy to ensure feasibility. In addition, a greedy policy that transitions smoothly from the nominal control is proposed to reduce the conservativeness of the common backup policy. Under the proposed method, time-invariant and input constraints are always satisfied. Although time-varying constraints may not always be fulfilled due to their aggressive dynamics, the proposed method demonstrates farsighted maneuvers through the backup trajectory computed over the receding horizon. When the backup trajectory approaches or violates constraints, the proposed method permits only safer inputs than the stop strategy, facilitating a return to the safe set by greedy policy while adhering to other constraints. The effectiveness of the proposed method was validated through simulations and experiments.