T$^\star$: Time-Optimal Risk-Aware Motion Planning for Curvature-Constrained Vehicles

This letter addresses the time-optimal risk-aware motion planning problem for curvature-constrained variable-speed vehicles in the presence of obstacles. To the best of our knowledge, this problem has not been solved. To obtain a feasible solution, we present a grid-based method, called T*, which computes the time-optimal risk-aware path by finding the optimal sequence of vehicle states from the start to the goal with the minimum total cost of time and risk. We propose a novel risk function based on the concept of collision time, which utilizes the complete information of the vehicle state, including its location with respect to obstacles, heading angle, and speed. We also propose a state pruning technique that can significantly reduce the computational complexity. The algorithm was validated in simulations of complex obstacle-rich scenarios, and the resulting paths are shown to be superior than the Dubins paths.