Trajectory planning for mechanical systems based on time-reversal symmetry

Abstract

The generation of feasible trajectories poses an eminent task in the field of control design in mechanical systems. The paper demonstrates innovative approach in trajectory planning for mechanical systems via time-reversal symmetry. It also presents two case studies: mass-spring-damper and inverted pendulum on the cart. As real systems break the time-reversal symmetry, the authors of this work propose a unique method in order to overcome this drawback. It computes a feed-forward reference control signal and state trajectories. The proposed solution enables compensation for the effects of couplings, which break the time-symmetry by a special proposed measure. The method suppresses the overall open-loop accumulated error and produces high-quality favorable control and state trajectories. Furthermore, the existence of the designed control signal and state trajectories is guaranteed if the equations of the motion have a solution in the direct flow of time.