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

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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.

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Acknowledgments

I would like to thank Joshua Willman who comes from America for the great help to correct the English.

Author information

Correspondence to Rong Xiong.

Additional information

This work was supported by the National Nature Science Foundation of China (Grant No. 61473258 and Grand No. U1609210)

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Zhao, Y., Xiong, R. & Zhang, Y. Model Based Motion State Estimation and Trajectory Prediction of Spinning Ball for Ping-Pong Robots using Expectation-Maximization Algorithm. J Intell Robot Syst 87, 407–423 (2017). https://doi.org/10.1007/s10846-017-0515-8

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Keywords

  • Expectation-maximization
  • Gaussian mixture model
  • Motion state estimation
  • Spinning-flying ball
  • Trajectory prediction