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Safety is one of the fundamental problems in robotics. Recently, a quadraticprogram-based control barrier function (CBF) method has emerged as a way toenforce safety-critical constraints. Together with control Lyapunov function(CLF), it forms a safety-critical control strategy, named CLF-CBF-QP, which canmediate between achieving the control objective and ensuring safety, whilebeing executable in real-time. However, once additional constraints such asinput constraints are introduced, the CLF-CBF-QP may encounter infeasibility.In order to address the challenge that arises due to the infeasibility, wepropose an optimal-decay form for safety-critical control wherein the decayrate of the CBF is optimized point-wise in time so as to guarantee point-wisefeasibility when the state lies inside the safe set. The proposed controldesign is numerically validated using an adaptive cruise control example.

Safety-Critical Control using Optimal-decay Control Barrier Function with Guaranteed Point-wise Feasibility