Exponential Barrier Functions for Safe Steering of Nonholonomic Vehicles With Actuator Time-Delay

This work provides a provably safe feedback control for nonholonomic vehicles that autonomously operate in an obstacle field. A barrier function with a tunable, exponential decay rate is used to obtain a safe steering envelope for the vehicle. The safe steering envelope adapts, in real-time, to the vehicle's velocity and its distance to the static obstacles. The safety control corrects steering commands provided by a nominal tracking control and prevents collisions between the vehicle and the obstacles. The safety and stability of the algorithm are proved analytically and verified via multiple experiments. The resulting safety control is modular and can work well with obstacles of different footprints. Since quick steering control is essential for successful vehicle navigation, a two-layer predictor is proposed to compensate for the time-delay in the vehicle dynamics. The two-layer predictor improves the control response time by as much as a factor of four. The safety and tracking control act on the vehicle kinematics, and the two-layer predictor improves the vehicle's dynamic performance. The proposed control structure has a closed-form with eight tunable parameters, which facilitates control calibration and tuning in large systems of vehicles. Extensive experiments are carried out on a nonholonomic vehicle to verify the effectiveness of the proposed algorithm.