Time Optimum Motion Planning for a Set of Car-Like Robots

This paper presents a global solution for simultaneously planning of time optimum motions for a set of car-like robots, which are moving on a two-dimensional general terrain. The method obtains the geometric paths and vehicles speeds that simultaneously minimize motion time for all the robots, considering robots’ kinodynamics (kinematic and dynamic constraints) and terrain geometry (terrain topography and obstacles). The proposed method is based on the Bump-Surface concept where the robots’ environment is represented by a higher dimension B-Spline surface and the robots’ paths consist of B-Spline curves mapped to the initial robots’ environment. A global optimization problem is then formulated considering simultaneously the optimal time motion and path planning between the obstacles for all the robots. The performance of the proposed method is investigated and discussed through simulated experiments.