In this paper, we propose a safety-critical controller based on time-varying control barrier functions (CBFs) for a robot with an unicycle model in the continuous-time domain to achieve navigation and dynamic collision avoidance. Unlike previous works, our proposed approach can control both linear and angular velocity to avoid collision with obstacles, overcoming the limitation of confined control performance due to the lack of control variable. To ensure that the robot reaches its destination, we also design a control Lyapunov function (CLF). Our safety-critical controller is formulated as a quadratic program (QP) optimization problem that incorporates CLF and CBFs as constraints, enabling real-time application for navigation and dynamic collision avoidance. Numerical simulations are conducted to verify the effectiveness of our proposed approach.

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