Control Safety Function for Explicit Safety-Critical Control of Autonomous Vehicles

Real-time safety-critical control is essential for high-level autonomous driving. Existing methods usually formulate safety-critical control as a constrained optimal control problem (COCP), and suffer from high computational complexity of the underlying iterative optimization processes. To address the issue of complexity, this paper presents an explicit safety-critical control method called the Control Safety Function (CSF) approach, which can replace online optimization with an analytical control law, dramatically enhancing real-time control capabilities. The CSF is formulated as the weighted sum of Control Lyapunov Function (CLF) and Control Barrier Functions (CBFs), with the value of CSF increasing to infinity as the state approaches the boundary of a safe set. The explicit control law is then derived from the gradient of CSF and system dynamics. Different from existing explicit controllers that can only apply to systems of relative degree one, the CSF method provides an approach to enforce safety constraints to systems with high relative degree, making CSF especially suitable for autonomous driving. The CSF approach is evaluated in a vehicle path-tracking scenario with multiple obstacles, accompanied by a comparative analysis against the Model Predictive Control (MPC) method. Simulation results indicate that CSF achieves control accuracy comparable to MPC, with significant reduction in computation time - approximately 3.23 ms per step, which is about 94.0% faster. These results suggest that CSF is a promising approach for real-time safety-critical control of high-level autonomous driving.