An online trajectory planning of struck ball with spin by table tennis robot

Abstract

This paper is concerned with an online trajectory planning of a ping-pong ball struck by a racket of a robotic table tennis system, which can detect the coming ball and predict the striking point by the racket. The struck ball trajectory is determined by the rebound phenomenon on the racket and the flying motion with the air resistances, which are governed by physical models of a racket rebound model (RRM) and an aerodynamics model (ADM) respectively. Therefore, the racket motion for the desired struck ball trajectory is obtained by solving the ADM and the RRM sequentially backward in time. Especially, the two point boundary value problem (TPBVP) of the ADM has to be solved for a desired landing point in the opponent's court. The finite difference method (FDM) for the TPBVP leads to a set of nonlinear simultaneous equations because of the ADM's nonlinearity while the ball motion at the striking point as one of the boundaries is constrained by a condition which guarantees the existence of the solution of the RRM. Therefore, we propose an novel method where the set of simultaneous equations by the FDM is formulated as a time-varying one and it is linearized by replacing the time-varying terms to the time sequence of an analytical solution of an approximated ADM. This linearized equations are solved iteratively to improve the accuracy and to satisfy the constraint. The processing time and the accuracy are verified by numerical examples where the algorithm is coded by C++ Language.