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In this paper, we propose a safety-critical controller based on time-varyingcontrol barrier functions (CBFs) for a robot with an unicycle model in thecontinuous-time domain to achieve navigation and dynamic collision avoidance.Unlike previous works, our proposed approach can control both linear andangular velocity to avoid collision with obstacles, overcoming the limitationof confined control performance due to the lack of control variable. To ensurethat the robot reaches its destination, we also design a control Lyapunovfunction (CLF). Our safety-critical controller is formulated as a quadraticprogram (QP) optimization problem that incorporates CLF and CBFs asconstraints, enabling real-time application for navigation and dynamiccollision avoidance. Numerical simulations are conducted to verify theeffectiveness of our proposed approach.

Obstacle Avoidance for Unicycle-Modelled Mobile Robots with Time-varying Control Barrier Functions