Event-Time Hybrid Optimal Control for Robotic Table Tennis Serves

2026-08-08

AI Summary

This work addresses the challenge of generating fast, highly spinning table tennis serves that comply with game rules and respect robotic dynamic constraints. The problem is formulated as an event-driven time-optimal control problem, jointly optimizing the hitting time, racket velocity, and orientation while explicitly embedding nonlinear event constraints such as ball flight, bounce, and net clearance. The proposed event-driven hybrid optimal control framework enforces physical constraints directly at phase boundaries, significantly improving computational efficiency and guaranteeing trajectory feasibility. Experimental results demonstrate a 4.1× speedup in solution time, with a mean landing error of 13.1 ± 7.3 cm, and successful execution of diverse spin serves reaching up to 30 revolutions per second.

Abstract

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.

Problem

• robotic table tennis
• optimal control
• kinodynamic constraints
• spin control
• hybrid dynamics

Innovation

• event-time optimal control
• hybrid dynamics
• spin-controlled serving
• kinodynamic feasibility
• table tennis robotics