Model Based Motion State Estimation and Trajectory Prediction of Spinning Ball for Ping-Pong Robots using Expectation-Maximization Algorithm
Model Based Motion State Estimation and Trajectory Prediction of Spinning Ball for Ping-Pong Robots using Expectation-Maximization Algorithm
复制标题
使用期望最大化算法的基于模型的乒乓机器人旋转球的运动状态估计和轨迹预测
DOI：
10.1007/s10846-017-0515-8
复制
发表时间：
2017-09-01
影响因子：
3.3
通讯作者：
Zhang, Yifeng
中科院分区：
文献类型：
--
作者：
Zhao, Yongsheng;Xiong, Rong;Zhang, Yifeng
运动状态“乒乓球的运动状态包括飞行状态和旋转状态。“对旋转球的估计和轨迹预测是推动下一代机器人乒乓球系统和旋转飞行物体运动分析研究的两个重要但具有挑战性的问题。由于马格努斯力作用在球上，飞行状态“飞行状态”表示实时平移速度。“和自旋状态“自旋状态表示实时旋转速度。“是相互关联的，这使得准确估计它们成为一个巨大的挑战。在本文中，我们首先推导出扩展连续运动模型（ECMM）的聚类轨迹到多个类别与K-均值算法和拟合他们分别使用傅立叶级数。ECMM可以很容易地适应各种轨迹。基于ECMM，我们提出了一种新的运动状态估计方法，使用期望最大化（EM）算法，从而有助于准确的轨迹预测。在该方法中，ECMM中的类别被视为一个潜在的变量，和运动状态的可能性被制定为一个高斯混合模型（GMM）的轨迹预测和观察之间的差异。所提出的方法的有效性和准确性进行了验证，离线评估使用收集的数据集，以及在线评估，人形机器人乒乓球系统“吴&孔”成功地击中高速旋转的球。
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.