Robotic Table Tennis

Unlike singles, humanoid table tennis doubles requires teammates to strike in strict alternation while sharing a confined workspace. Rapid repositioning can compromise striking accuracy, while uncoordinated teammate movements introduce collision risks. We present PingpongDuo, a hierarchical framework for agile humanoid doubles with safe team coordination. At the team level, a planner jointly selects positioning targets and uses learned risk estimates to filter risky proposals, preferentially preserving the current striker's target. At the individual level, separate footwork and striking skills combine agile movement with precise racket control. The skills are guided by human motion references, including footwork collected from human doubles play, and trained from states produced by one another to support rapid transitions. A racket-arm residual further refines strikes after movement using return feedback from a simulator calibrated with real ball-flight and contact measurements. In simulation, PingpongDuo improves the ball-return success rate by 13.2% over the state-of-the-art baseline, while achieving approximately 2 cm positioning error during clearance. In real-world experiments, a robot completes a 2.15 m clearance-and-recovery cycle in 2.4 s with a peak speed of 2.23 m/s, while two robots sustain more than 10 consecutive strikes in strict alternation.

Competitive humanoid table tennis requires two distinct abilities: executing a desired return and deciding where to return the ball. We separate these two problems, with the ball landing target serving as an interface between motor control and strategy. (1) We first train a whole-body motor policy conditioned on the desired landing target, which maps the target to an executable humanoid stroke through a model-based strike planner and a learned controller. (2) We then improve the motor policy through self-play in closed-loop rallies, where the robot learns to handle incoming balls generated by another player rather than only prescribed incoming balls. At this stage, the landing targets are still sampled without considering the opponent, so the policy improves its execution without learning game strategy. (3) Finally, we freeze the entire motor stack and train a stroke-level strategic policy to choose landing targets through competitive self-play. Motor self-play improves both landing accuracy and legal-return rate during rallies. More importantly, with the entire motor stack fixed, changing only the target-selection policy leads to large differences in game outcomes: the learned strategy wins 89%, 82%, and 73% of points against center, random, and away-from-opponent baselines, respectively. The learned strategy also changes where it sends the ball according to the opponent's position and the previous target, showing that self-play learns more than simply aiming at fixed "good" locations. On hardware, the same frozen execution stack and strategic interface support complete 11-point games against a recreational human opponent, including multi-stroke rallies with both forehand and backhand returns.

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 30rps. These results show that event-time optimal control efficiently generates physically valid, kinodynamically feasible serves while accounting for nonlinear aerodynamic and impact effects.

Table tennis, a dynamic, compact, and popular sport, has received significant attention as a robotics benchmark over the last decades. Most of the research has focused on the rally aspect - returning an incoming ball - requiring high-speed vision, agile motion planning, and tight closed-loop control. However, the other component of table tennis gameplay - the serve - is comparatively a quite unexplored research problem, that in fact requires pushing physics modeling and control to the extremes. Achieving competitive serves with a robot presents domain-specific challenges, such as high-spin generation from a spinless ball, precise aiming, or multi-objective optimization. In this work, we present a novel approach for generating official rule-compliant serves by combining motion primitives, Model Predictive Control, and Bayesian Optimization. Serves generated in this way offer a wide and controllable variation of spins of up to 550 rad/s, and speeds of up to 6.7 m/s, matching and even surpassing those of elite table tennis players.

At competitive speeds and spins, a table tennis ball follows complex, counterintuitive trajectories that a robot must track and precisely counter within fractions of a second. Training a reinforcement learning policy capable of these skills is prohibitively expensive and dangerous in the real world, making high-fidelity simulation essential. Transferability of such policies, however, critically depends on how faithfully the simulation captures real-world dynamics - a requirement made even more stringent by the adversarial nature of the game, where any modeling inaccuracy becomes an exploitable weakness for the opponent. Prior state-of-the-art in robot table tennis generally focuses on a limited range of velocities and spins and fails to capture the richness of ball behaviors encountered in professional-level play. In this work, we present physics models for aerodynamic ball flight, ball-table contact, and ball-racket contact. that accurately capture the ball behavior over a vast range of speeds and spins relevant to the game. Specifically, we model drag and Magnus force coefficients as functions of Reynolds number and spin ratio in the aerodynamics equations. For the table contact model we model effects of ball buckling on the coefficient of restitution and incorporate residuals into the instantaneous point-contact models. For the racket contact model, we introduce a residual neural network component to complement coefficients related to normal and tangential coefficients of restitution as well as torsional spin damping. Evaluated on an unprecedentedly large dataset of competitive matches (277 games), the proposed models significantly reduces prediction errors (e.g., 59% median landing-position error reduction). The resulting models were used to train the RL policies for the first real-world robot table tennis AI agent capable of competing against professional players.

This paper focuses on the hardware specifications required for a table tennis robot to beat professional players. After analyzing the motions of elite players, we defined target specifications for the workspace, payload, external-force resistance, physical performance, serve capability, and end-effector accuracy. Based on these specifications, we developed "Ace", a custom 8-DoF robot. The mechanical structure was improved through topology optimization to minimize mass while preserving stiffness. Motor and gearbox selection was optimized using an inverse-dynamics torque model. Low-order per-joint dynamics models with delay compensation were identified and integrated into simulation to enable the use of an RL control policy. Experiments demonstrated repeated full-stroke swings with a cycle time of 0.8 s and a peak racket-center velocity of 22 m/s. The robot successfully defeated multiple professional players.

Robotic table tennis has emerged as a compelling benchmark for real-time robotic perception due to its fast ball dynamics and stringent timing requirements. Accurate, high-frequency, and low-latency ball state estimation is critical for reliable trajectory prediction and timely control. Traditional frame-based cameras face an inherent trade-off: low frame rates leave temporal blind spots that miss fast-moving objects and high frame rates raise data and computational cost. Event cameras instead offer microsecond temporal resolution and, under sufficient illumination, remain largely free of motion blur even at high ball speeds. However, the community lacks large-scale datasets to develop and benchmark event-based perception in realistic sports scenarios. We address this gap by introducing the first large-scale event-camera dataset for table tennis, comprising over 1000 rallies from a diverse group of players ranging from amateurs to elite-level athletes. Each recording captures the event stream alongside 14 synchronized high-speed frame-based cameras at 200 FPS, which we use to produce 1 kHz pseudo ground-truth labels for ball position, velocity, and spin. Building on this dataset, we train a convolutional neural network robust to background player motion that jointly estimates the ball's position and velocity in the image-plane from events. Treating the predicted velocity as an additional measurement in the Kalman filter reduces bounce-point prediction error by 36% relative to a position-only baseline. Finally, we close the perception-action loop by integrating the event-based system with a Stäubli robotic arm, enabling the first real-time human-robot table tennis rallies driven by event-based perception.

Robotic table tennis is a representative benchmark for high-speed, closed-loop robotic control in dynamic environments, where accurate and fast prediction of ball states is critical for reliable planning and control. Physics-based approaches rely heavily on accurate parameter identification and precise initial state, while learning-based methods often struggle to capture long-range temporal dependencies and are typically trained on limited or simulated data. We propose a transformer-based framework for table tennis ball state prediction that leverages attention mechanisms to model long-range temporal correlations directly from historical observations, without relying on explicit flight or bounce models. To support robust learning and generalization, we collected a large-scale real-world dataset from players of varying skill levels and diverse ball cannon configurations. The combination of a high-capacity transformer architecture and extensive real-world data enables accurate long-horizon forecasting. Building on this capability, we introduce a plug-and-play sim-to-real transfer strategy, Swap Predictor at Deployment (SPAD), which replaces the physics-based simulator used during training with the proposed real-world-trained predictor at deployment, improving the sim-to-real transferability of the policy without requiring retraining. We demonstrate that this simple substitution effectively narrows the sim-to-real gap while preserving the efficiency and scalability of simulation-based training.

Accurate dynamic models for racket-ball bounces are essential for reliable control in robotic table tennis. Existing models typically assume simple linear models and are restricted to inverted rubbers, limiting their ability to generalize across the wide variety of rackets encountered in practice. In this work, we present a unified framework for modeling ball-racket interactions across 10 racket configurations featuring different rubber types, including inverted, anti-spin, and pimpled surfaces. Using a high-speed multi-camera setup with spin estimation, we collect a dataset of racket-ball bounces spanning a broad range of incident velocities and spins. We show that key physical parameters governing rebound, such as the Coefficient of Restitution and tangential impulse response, vary systematically with the impact state and differ significantly across rubbers. To capture these effects while preserving physical interpretability, we estimate the parameters of an impulse-based contact model using Gaussian Processes conditioned on the ball's incoming velocity and spin. The resulting model provides both accurate predictions and uncertainty estimations. Compared to the constant parameter baselines, our approach reduces post-impact velocity and spin prediction errors across all racket types, with the largest improvements observed for nonstandard rubbers. Furthermore, the GP-based model enables online identification of racket dynamics with few observations during gameplay.

Perception and decision-making in high-speed dynamic scenarios remain challenging for current robots. In contrast, humans and animals can rapidly perceive and make decisions in such environments. Taking table tennis as a typical example, conventional frame-based vision sensors suffer from motion blur, high latency and data redundancy, which can hardly meet real-time, accurate perception requirements. Inspired by the human visual system, event-based perception methods address these limitations through asynchronous sensing, high temporal resolution, and inherently sparse data representations. However, current event-based methods are still restricted to simplified, unrealistic ball-only scenarios. Meanwhile, existing decision-making approaches typically require thousands of interactions with the environment to converge, resulting in significant computational costs. In this work, we present a biologically inspired approach for high-speed table tennis robots, combining event-based perception with sample-efficient learning. On the perception side, we propose an event-based ball detection method that leverages motion cues and geometric consistency, operating directly on asynchronous event streams without frame reconstruction, to achieve robust and efficient detection in real-world rallies. On the decision-making side, we introduce a human-inspired, sample-efficient training strategy that first trains policies in low-speed scenarios, progressively acquiring skills from basic to advanced, and then adapts them to high-speed scenarios, guided by a case-dependent temporally adaptive reward and a reward-threshold mechanism. With the same training episodes, our method improves return-to-target accuracy by 35.8%. These results demonstrate the effectiveness of biologically inspired perception and decision-making for high-speed robotic systems.

Existing humanoid table tennis systems remain limited by their reliance on external sensing and their inability to achieve agile whole-body coordination for precise task execution. These limitations stem from two core challenges: achieving low-latency and robust onboard egocentric perception under fast robot motion, and obtaining sufficiently diverse task-aligned strike motions for learning precise yet natural whole-body behaviors. In this work, we present \methodname, a modular system for agile humanoid table tennis that unifies scalable whole-body skill learning with onboard egocentric perception, eliminating the need for external cameras during deployment. Our work advances prior humanoid table-tennis systems in three key aspects. First, we achieve agile and precise ball interaction with tightly coordinated whole-body control, rather than relying on decoupled upper- and lower-body behaviors. This enables the system to exhibit diverse strike motions, including explosive whole-body smashes and low crouching shots. Second, by augmenting and diversifying strike motions with a generative model, our framework benefits from scalable motion priors and produces natural, robust striking behaviors across a wide workspace. Third, to the best of our knowledge, we demonstrate the first humanoid table-tennis system capable of consecutive strikes using onboard sensing alone, despite the challenges of low-latency perception, ego-motion-induced instability, and limited field of view. Extensive real-world experiments demonstrate stable and precise ball exchanges under high-speed conditions, validating scalable, perception-driven whole-body skill learning for dynamic humanoid interaction tasks.

Musculoskeletal robots provide superior advantages in flexibility and dexterity, positioning them as a promising frontier towards embodied intelligence. However, current research is largely confined to relative simple tasks, restricting the exploration of their full potential in multi-segment coordination. Furthermore, efficient learning remains a challenge, primarily due to the high-dimensional action space and inherent overactuated structures. To address these challenges, we propose Diff-Muscle, a musculoskeletal robot control algorithm that leverages differential flatness to reformulate policy learning from the redundant muscle-activation space into a significantly lower-dimensional joint space. Furthermore, we utilize the highly dynamic robotic table tennis task to evaluate our algorithm. Specifically, we propose a hierarchical reinforcement learning framework that integrates a Kinematics-based Muscle Actuation Controller (K-MAC) with high-level trajectory planning, enabling a musculoskeletal robot to perform dexterous and precise rallies. Experimental results demonstrate that Diff-Muscle significantly outperforms state-of-the-art baselines in success rates while maintaining minimal muscle activation. Notably, the proposed framework successfully enables the musculoskeletal robots to achieve continuous rallies in a challenging dual-robot setting.