Fastest Planar Motion Trajectories with Unlimited Curvature
Aleksandr Sergeevich Bortakovskii · Journal of Computer and Systems Sciences International · 2022
Abstract The problem of speed is considered for a controlled dynamic system of the fifth order, which describes planar motion with limited acceleration. The motion trajectories of the proposed model differ from the Markov–Dubins paths, the trajectories of the Isaacs, Reeds–Shepp cars, etc., by their unlimited curvature, i.e., rotations (turning) on the spot are allowed. Such a model more accurately describes the capabilities of some types of road cars and aircraft. The angular velocity of the model changes continuously, thereby eliminating the jumps in angular velocity that are characteristic of the trajectories of the Dubins car and its generalizations. The optimal speed trajectories of the proposed model are described. Examples of the shortest trajectories that fall into the given terminal position (target) are given.