State Estimation And Trajectory Prediction Of Spinning-Flying Ping-Pong Ball

Motion state estimation and trajectory prediction of flying-spinning objects are one of the main challenges in real-time sensing and motion planning.It involves several key techniques in robotics,i.e.,the real-time detection and localization,motion model,rebound model,motion state estimation,trajectory prediction,motion decision,and motion planning.For a robot to play spinning ball,this paper conducted researches on the motion model,rebound model,motion state optimal estimation and trajectory prediction of a flying-spinning ping-pong ball and further verified the proposed models and algorithms in the humanoid robotic table tennis system"Wu&kong".This work was sponsored by National Natural Science Foundation.The main contributions are as follows.(1)Based on the force analysis,we proposed a motion model of a spinning ping-pong ball that sufficiently takes the spin effect into account,derived its corresponding continuous form,and proposed an optimal motion state estimation method using Gradient Descent Method(GDM).Using a Fourier series to fit the decay curve of flying velocity with respect to time,the analytically unsolvable differential equations was transformed into solvable differential equations.Solve it and we can derive the continuous motion model.Comparing to the discrete one,the continuous motion model can directly predict the motion state of a ping-pong ball at any time in the future without iteration.Therefore,it effectively eliminates the iterative error.Based on the continuous motion model,we propose a novel motion state estimation method that can search the optimal motion state using GDM by minimizing the Euclidean distance between trajectory observations and predictions.Compared to the existing methods,e.g.,polynomial fitting and local weighted regression,our method is model-based and can effectively use consecutive frames of trajectory observations to estimate the motion state,which is more accurate and robust.(2)The motion model is high-order and nonlinear,thus using one Fourier series to fit the decay ratio of flying velocity with various motion state is not accurate.In this paper,we derive an Extended Continuous Motion Model(ECMM)by clustering the trajectories into multiple categories with a K-means algorithm and fitting them respectively using several Fourier series.Based on the ECMM,we propose a novel motion state estimation method using Expectation-Maximization(EM)algorithm,which in result contributes to a more 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 trajectory predictions and ob-servations.The effectiveness and accuracy of the proposed method is verified using a collected dataset(3)Considering the collision between a ball and a table as a gradual process,a nonlinear rebound model was proposed based on the momentum theorem,angular momentum theorem and mean value theorem,which the forces acting on a ball are formulated as continuous functions.The unknown functions in the model are effectively identified using multilayer perception.Due to fiction force,the flying velocity and spinning velocity would affect with each other.And the collision period is very short Then,thus there is nearly no sensors that can measure the change of motion state and forces acting on the ball effectively and accurately.The novelty of the proposed model is that the forces and the parameters in it are formulated as the continuous functions related to the ball' s motion state,which is more accurate,rather than as constants.The integrations of these functions over time can be formulated by using the mean value theorem,and their expressions are learned using multilayer perception with a large data set collected by the position vision system and the pan-tilt vision system.The experimental results verify the effectiveness and accuracy of the proposed model.Using the proposed motion model,rebound model and motion state estimation methods,the robotic table tennis system can perceive a high-speed flying-spinning ping-pong ball with high accuracy in real-time.The prediction accuracy at collision point in x-and y-axis are 1.36cm and 2.95cm ans the estimation accuracy of spin state in x-and z-axis are 5.36rad/s and 2.97rad/s.The predicted hitting point in a 3cm radius circle around the center of racket is 44.06%,in a 5cm radius circle is 84.30%,and in the racket(7.5cm)is 95.55%.We further test the proposed models and methods by serving the robotic table tennis system "Wu" to play high-speed spinning ball with a success rate of 71.2%.