Motion generation for robots in highly dynamic environments is challenging due to the need for high efficiency and error tolerance. Robots must generate motion efficiently within milliseconds to react to environmental changes swiftly. Furthermore, the limitations of perceptual systems in detecting fast-moving objects necessitate robust motion generation that can tolerate perceptual errors. This paper presents a motion generation framework that ensures both high efficiency and error tolerance for the dynamic task of robotic table tennis. To achieve high efficiency, this study introduces a novel analytical solution to the ball flight equation using Chebyshev approximation, offering a time complexity of O (1). For robotic motion generation, this study proposes a dimension-reduced task planner and employs piecewise cubic polynomial and Variable-Sigmoid-Based motion templates for individual joint motions, with coefficients determined analytically and rapidly. To enhance perceptual error tolerance, this study develops a policy optimizer based on a striking-at-the-center principle. The proposed task planner accelerates paddle motion determination by an average of 9.27 times. The proposed ball motion prediction method enhances the efficiency of determining the ball-paddle collision point by up to a factor of two. Additionally, the proposed framework improves the success rate of planning and striking by 16.0% and 18.3%, respectively, compared to methods that do not account for error tolerance. It also reduces the landing position error in the x and y directions by 32.5% and 35.6%, while improving the accuracy of passing-net height by 24.0%.
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