Optimal State Estimation of Spinning Ping-Pong Ball Using Continuous Motion Model

Abstract

Precise trajectory prediction is a fundamental issue for ping-pong robot systems. Due to the difficulty of spin estimation and the complexity of the motion model, most existing algorithms ignore the effect of spin, which will result in a significant deviation in trajectory prediction of spinning ping-pong ball. Some literatures proposed to estimate spin state based on trajectory bias, but due to the limitations of the discrete motion model they derived, only polynomial fitting method can be used for spin estimation, rather than model-based method, which will cause inaccurate spin estimation and trajectory prediction. In this paper, we derive a continuous motion model (CMM) of spinning ping-pong ball based on forces analysis. During the derivation, the Fourier series is used to fit the velocity changing over time, which transforms the model from unsolvable coupled variable-coefficient differential equations to solvable uncoupled equations. On the strength of the CMM, a model-based optimal algorithm for ball's motion state <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> estimation is proposed. Using the initial trajectory acquired by a stereo vision system, the proposed method first estimates the motion state approximately with polynomial fitting, and then uses gradient descent method to achieve a model-based optimal estimation by minimizing a cost function corresponding to the differences between trajectory predictions and observations. We also prove that this optimization problem can be plotted as a convex optimization problem; thus, the globally optimal solution can be obtained. The experimental results confirm the effectiveness and accuracy of the proposed method.