High Speed Robotic Table Tennis Swinging Using Lightweight Hardware with Model Predictive Control

TL;DR

The paper tackles the challenge of dynamic, high-speed manipulation in robotic table tennis by integrating a lightweight 5-DoF anthropomorphic arm with a fixed-horizon model predictive control framework to generate and track swing trajectories. A ball trajectory prediction module (based on simplified flight-bounce dynamics) provides terminal strike constraints (position, velocity, and paddle orientation), which the MPC uses to compute end-to-end swing plans. The authors compare Shrinking Horizon and Fixed Horizon MPC implementations and demonstrate that Fixed Horizon with warm starts offers faster convergence and greater reactivity, enabling robust execution of loop, drive, and chop hits. Hardware experiments show average ball exit speeds up to $11$ m/s with hit rates approaching $88-89\%$ across swing types, indicating substantial progress toward human-level performance in robotic table tennis and dynamic manipulation tasks.

Abstract

We present a robotic table tennis platform that achieves a variety of hit styles and ball-spins with high precision, power, and consistency. This is enabled by a custom lightweight, high-torque, low rotor inertia, five degree-of-freedom arm capable of high acceleration. To generate swing trajectories, we formulate an optimal control problem (OCP) that constrains the state of the paddle at the time of the strike. The terminal position is given by a predicted ball trajectory, and the terminal orientation and velocity of the paddle are chosen to match various possible styles of hits: loops (topspin), drives (flat), and chops (backspin). Finally, we construct a fixed-horizon model predictive controller (MPC) around this OCP to allow the hardware to quickly react to changes in the predicted ball trajectory. We validate on hardware that the system is capable of hitting balls with an average exit velocity of 11 m/s at an 88% success rate across the three swing types.

Figures (9)

• Figure 1: Hardware Strikes. Loop (top), drive (middle), and chop (bottom) with exit ball trajectory shown.
• Figure 2: Modified MIT Humanoid Arm. The arm shoulder consists of $q_1$-$q_3$ with directly connected actuators while the $q_4$ actuator controls the elbow with a short belt transmission. $q_5$ is a smaller Dynamixel motor since it requires little torque to orient the paddle.
• Figure 3: Arm workspace analysis. The black outline represents all achievable positions while the colored region is a heat map of the average orientation error bounded to 10°. The discolored region near $Y=-0.4$, $Z=-0.2$ is due to the wrist and first shoulder DoFs being close to singularity making some orientations difficult to reach.
• Figure 4: System Communication Diagram. In blue, the Windows machine runs the OptiTrack Motive software which is responsible for reading the cameras, capturing marker data, and publishing it over the NatNet network. A separate Linux Hub Computer (HC), in yellow, receives and filters the marker data then publishes it over LCM in the OptiTrack Listener process. Also on the HC, the Prediction Process computes the expected ball state as it reaches the arm which is then sent through LCM to a second Linux Arm Computer (AC). The AC, in green, receives the prediction in the Main Process and then interfaces with the Optimization Process to receive a new trajectory based on the strike conditions. Finally, the Main Process sends arm commands to the Arm Communication Process which handles low-level control and interfaces with the hardware via Ethernet and CAN on a middleware board.
• Figure 5: Characterized Prediction Error. The top and bottom plots show the distribution errors in $\mathbf{p_{des}}$ and $t_{strike}$ respectively as the ball approaches the strike-plane. The blue shaded region indicates the times where 90% of the balls bounce, the green line marks when a 0.5 second swing begins, and the red line is the critical error of 7.5 cm of the paddle radius.