Obstacle Avoidance in Path Following using Local Spline Relaxation

This paper presents a motion planning approach, Local Spline Relaxation with Local Hyperplanes (LSR-LH), for autonomous vehicles to search for time-optimal collision-free motion trajectories through environments with stationary and dynamic convex obstacles. These trajectories are piecewisely parameterized as a fourth order polynomial based on Runge-Kutta's fourth order integration scheme. Collision-free trajectories are guaranteed by defining separating hyperplanes between obstacles and the continuous time trajectory of the vehicle. An optimal control problem is solved with a receding horizon to include the latest information of the environment and to take into account model mismatches. Extensive numerical simulations are performed to show the potential of the method.