AI 中文总结
针对机器人乒乓球发球的非线性混合系统，提出事件时间最优控制方法，结合两个OCP生成符合约束的发球，求解时间缩短4.1倍，真实机器人实验实现可控落点与各类旋转发球。
AI 中文摘要
机器人乒乓球发球需要高球速和强旋转，同时要满足机器人的运动动力学极限。与对攻击球不同，有效发球必须在发球方一侧弹跳且越过球网，形成包含非线性飞行和碰撞动力学的混合系统。我们将旋转控制的发球生成建模为事件时间最优控制问题（OCP），该问题同时优化球拍碰撞速度、方向以及弹跳、过网和落地时间，可在表弹跳和过网约束的相位边界处直接执行。随后，通过第二个最优控制问题（OCP）将球拍速度和方向转换为完整的运动学可行运动，该OCP需满足关节位置、速度和力矩限制。我们通过数值模拟和KUKA Agilus机器人对该方法进行评估。与带根定位的固定步长公式相比，所提事件时间公式将中位数求解时间减少了4.1倍，同时保持了相当的落地精度、旋转精度和发球有效性。真实机器人实验展示了可控的落点以及上旋、下旋和侧旋发球，平均落地误差为$13.1 \textpm 7.3$cm，旋转速率可达30 rps。这些结果表明，事件时间最优控制可高效生成物理上有效、运动学可行的发球，同时考虑非线性空气动力学和碰撞效应。
英文摘要
Robotic table tennis serves require high ball velocity and spin while respecting the robot's kinodynamic limits. Unlike rally strokes, a valid serve must also bounce on the server's side and clear the net, yielding a hybrid system with nonlinear flight and impact dynamics. We formulate spin-controlled serve generation as an event-time \ac{OCP} that optimizes the racket impact velocity and orientation together with the bounce, net-crossing, and landing times, enabling direct enforcement at phase boundaries of table-bounce and net-clearance constraints. The racket velocity and orientation are then converted into a complete kinodynamically feasible motion through a second \ac{OCP} enforcing joint-position, velocity, and torque limits. We evaluate the method numerically and on a KUKA Agilus robot. Compared with a fixed-step formulation with root localization, the proposed event-time formulation reduces the median solve time by a factor of 4.1 while maintaining comparable landing accuracy, spin accuracy, and serve validity. Real-robot experiments demonstrate controlled placement and topspin, backspin, and sidespin serves, with a mean landing error of $13.1 \pm 7.3$~cm and spin rates up to 30~rps. These results show that event-time optimal control efficiently generates physically valid, kinodynamically feasible serves while accounting for nonlinear aerodynamic and impact effects.
