Model Based Motion State Estimation and Trajectory Prediction of Spinning Ball for Ping-Pong Robots using Expectation-Maximization Algorithm

Abstract

Motion state "Motion state of a ping-pong ball consists of the flying state and spin state." estimation and trajectory prediction of a spinning ball are two important but challenging issues for both the promotion of the next generation of robotic table tennis systems and the research on motion analysis of spinning-flying objects. Due to the Magnus force acting on the ball, the flying state "Flying state denotes the real-time translational velocity." and spin state "Spin state denotes the real-time rotational velocity." are coupled, which makes the accurate estimation of them a huge challenge. In this paper, we first derive the Extended Continuous Motion Model (ECMM) by clustering the trajectories into multiple categories with a K-means algorithm and fitting them respectively using Fourier series. The ECMM can easily adapt to all kinds of trajectories. Based on the ECMM, we propose a novel motion state estimation method using Expectation-Maximization (EM) algorithm, which in result contributes to an accurate trajectory prediction. In this method, the category in ECMM is treated as a latent variable, and the likelihood of motion state is formulated as a Gaussian Mixture Model (GMM) of the differences between the trajectory predictions and observations. The effectiveness and accuracy of the proposed method is verified by offline evaluation using a collected dataset, as well as online evaluation that the humanoid robotic table tennis system "Wu & Kong" successfully hits the high-speed spinning ball.