To improve and validate the performance of humanoid robot, the research on a table-tennis game by both humanoid robots is supported by 863, the national hi-tech program. Due to the limitation of the visual feedback system and the motion ability of the humanoid robot, a precise model of the table-tennis game is necessary to predict the ball's trajectory. This paper details the dynamic model of the ball's flight trajectory as well as its parameters calibration by Photron Fastcam, a high speed camera with 2kfps to capture the trajectory of ball. With the model's characteristics, ball's flight trajectory prediction based on a few observation points is employed as well as its noise sources are discussed. According to the requirement of table-tennis game by humanoid robot, a novel nonlinear observer is developed to improve the prediction accuracy. Finally, Experiments results with binocular vision show that the model and trajectory prediction proposed by the paper outperform the requirement of the game.

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Optimal transportation plays a fundamental role in many fields in engineering and medicine, including surface parameterization in graphics, registration in computer vision, and generative models in deep learning. For quadratic distance cost, optimal transportation map is the gradient of the Brenier potential, which can be obtained by solving the Monge-Ampère equation. Furthermore, it is induced to a geometric convex optimization problem. The Monge-Ampère equation is highly non-linear, and during the solving process, the intermediate solutions have to be strictly convex. Specifically, the accuracy of the discrete solution heavily depends on the sampling pattern of the target measure. In this work, we propose a self-adaptive sampling algorithm which greatly reduces the sampling bias and improves the accuracy and robustness of the discrete solutions. Experimental results demonstrate the efficiency and efficacy of our method.