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打乒乓球对机器人来说是一项综合性挑战，尤其针对接打旋转球，对机器人的视觉系统、决策系统以及高速运动控制系统都提出了更高的要求。本文在已有机器人击打推挡球的基础上，重点针对机器人接打旋转球的问题进行研究，主要工作包括以下方面：

 

第一，围绕乒乓球机器人系统的机构改进设计与运动控制方法进行研究。首先，研制了一款五自由度轻型机械臂，安装在两自由度大范围平移底座上，构成了兼顾运动范围与灵活性的宏微运动平台；在此基础上，研究了滚动优化的运动规划方法，使机器人能够根据实时检测到的乒乓球轨迹，平滑、安全地在运动中修正自己的运动状态和后续路径，从而准确地完成击球动作。

 

第二，围绕多目视觉跟踪系统进行研究。首先，将高斯模型法与帧间差分法相融合，设计了一种新的乒乓球图像识别与跟踪算法，改善了视觉系统的鲁棒性和实时性；其次，基于乒乓球飞行轨迹特性，设计了无需摄像机间相互对时的乒乓球三维轨迹重建方法，减小多相机对时造成的误差，提高实时性；最后，提出了一种新的多目系统摄像机参数矫正方法，以提高各摄像机参数一致性为目标，改善乒乓球轨迹的重建精度。

 

第三，基于滚动优化的框架，提出了一种将物理模型与经验模型相融合的旋转球轨迹预测方法。首先,依靠基于乒乓球飞行动力学模型设计的时变扩展卡尔曼滤波算法，得到平滑和准确的乒乓球飞行轨迹；然后，设计了基于经验数据的无旋转与带旋转乒乓球轨迹预测方法，依靠乒乓球飞行中的受力特点对经验数据进行了降维处理，提升了经验模型的效率；在此基础上，提出了基于乒乓球动力学模型和两种经验模型相结合的分段轨迹预测方法，在乒乓球不同的飞行阶段采用不同的预测策略，从而稳定地预测旋转球轨迹。

 

第四，针对旋转球的定点回球问题，提出了一种将物理模型与增强学习相融合的机器人回球参数解算方法。首先，基于乒乓球的飞行轨迹估算其自转角速度，并利用高斯过程回归方法对旋转球的轨迹特征进行归纳；然后，利用乒乓球的轨迹预测模型生成回球状态经验库，并据此求解旋转球与球拍的碰撞模型，得到初始的回球参数；最后，利用基于成本正则化核回归（Cost-regularized Kernel Regression，\textbf{CrKR}）的增强学习方法对初始参数进行修正，从而提高了对回球落点的控制精度。基于以上研究，实现了机器人击打旋转球的落点控制。

 

最后，总结本文所取得的研究成果，并对下一步研究提出展望。

Playing table tennis is a comprehensive challenge for robots. Especially when the table tennis is with strong rotation. A higher performance of visual sensing systems, efficient decision-making systems, and high-speed motion control systems are highly recommended. In this paper, a table tennis robot with spinning motions is studied using a regular robot which can handle only the un-spinning ball. The main contributions of the research are listed as the following.

 

Firstly, a research on the robots' mechanical structure and motion planning method are introduced. A five-degree-of-freedom lightweight manipulator is developed. It is mounted on a two-degree-of-freedom planar motion platform, constituting a macro-micro robot system which can move in a large space and high flexibility. Based on this system, receding horizontal motion planning method is proposed. The method empowers the robot to adjust its movement states and the follow-up paths according to the real-time detected table tennis's ball trajectory, and thus the batting action can be completed accurately.

 

Secondly, the multi-camera visual tracking system is studied. In this part, a new image recognition and tracking algorithm of a table tennis's ball are designed. The method improves the robustness and real-time performance of the visual sensing system. And based on the characteristics of table tennis flight trajectory, a new space trajectory reconstruction method is proposed. The new method does not need synchronization of the cameras in the system, therefore it improves the accuracy and speed of trajectory reconstruction. Furthermore, a new algorithm for camera parameter adjustment in multi-camera systems is proposed. The algorithm improves the consistency of the parameters of the systems, resulting in improving the reconstruction accuracy of the table tennis's ball tracking.

 

Thirdly, based on the framework of receding horizon, a spinning ball trajectory prediction method is proposed. The method combines the physical model with the empirical model. In the first step, based on the table tennis flight dynamics model the time-varying extended Kalman filter algorithm is adopted, thus smooth and accurate table tennis trace are obtained. Then, the non-spinning and spinning table tennis trajectory prediction methods based on empirical data is designed. To improve the efficiency of empirical models, the dimensionality of empirical data is reduced according to the force characteristics of table tennis' trajectory. The mentioned methods are merged to be a newly proposed segment trajectory prediction method. The method consists of a table tennis dynamics model and two empirical models. Different predicting strategies are adopted in different stages of table tennis' trace, thus an accurate and stable prediction of the spinning ball's trajectory are verified.

 

Fourthly, to hit the spinning ball back to the desired location, a method of solving the robot's hitting parameters is proposed. The method combines the physical model with the enhanced learning. In the first step, the angular velocity of table tennis is estimated, and the trajectory characteristics of a spinning ball are generated by Gaussian Process Regression. Then, the trajectory prediction model of table tennis is adopted to generate the experienced database, and the collision model of the spinning ball and the racket is solved, therefore the initial hitting parameter is obtained. In the last step, the initial parameters are modified by the reinforcement learning method based on the Cost-regularized Kernel Regression which improves the accuracy of the landing position of the returned ball.

 

Finally, summarization of the research is addressed with discussions and the prospect of the future research.