⚡ electrical engineering

Ace! Motion Planning of Professional-Level Table Tennis Serves with a Robot Arm

This paper presents a novel framework combining motion primitives, Model Predictive Control, and Bayesian Optimization to enable a robot arm to generate professional-level, rule-compliant table tennis serves with spin and speed capabilities that match or exceed those of elite human players.

Original authors: Guillem Torrente, Guilherme Jorge Maeda, Divij Grover, Megumu Tsukamoto, Hamdi Sahloul, Peter Dürr

Published 2026-07-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Guillem Torrente, Guilherme Jorge Maeda, Divij Grover, Megumu Tsukamoto, Hamdi Sahloul, Peter Dürr

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a robot arm trying to learn how to play the world's fastest, most spin-heavy game of ping-pong. For years, scientists have taught robots how to return a ball that comes flying at them (like a goalie saving a penalty kick). But teaching a robot to serve—to toss the ball up and hit it with such perfect speed and spin that it's impossible to return—has been like trying to teach a toddler to throw a perfect curveball while blindfolded.

This paper introduces "Ace!", a new system that finally lets a robot serve like a world-class professional. Here is how they did it, broken down into simple concepts:

1. The Problem: The "Perfect Serve" is Hard

In table tennis, a serve is the only move a player has total control over. To make a great serve, you have to:

Toss the ball up (which is tricky because it wobbles).
Hit it with a racket moving at high speed.
Apply a massive amount of "spin" (making the ball curve in the air).
Make sure it bounces once on your side, then once on the opponent's side, without hitting the net.

Robots usually struggle here because they are stiff and precise, while a human serve is a fluid, explosive, and slightly messy motion. The robot needs to be precise enough to hit the ball, but flexible enough to create the chaotic physics of a spinning ball.

2. The Solution: A Three-Part Recipe

The team built a system that combines three different "tools" to solve this puzzle:

The Motion Planner (The Choreographer):
Think of this as a dance instructor. It calculates the exact path the robot's arm needs to take. It doesn't just say "move arm here"; it breaks the movement down into tiny, smooth steps (like a movie made of 32 frames per second) to ensure the arm moves smoothly without jerking or breaking. It plans the path from the starting position to the exact moment of hitting the ball, and then how to stop safely.
The Physics Simulator (The Crystal Ball):
Before the robot actually hits a ball, this system runs thousands of "what-if" scenarios in a computer. It asks: "If I hit the ball this hard with this much spin, where will it land?" It checks if the ball hits the net, if it goes out of bounds, or if the robot's arm crashes into the table.
The AI Optimizer (The Coach):
This is the brain of the operation. They used a smart algorithm called HEBO (which is like a super-smart trial-and-error coach).
- The coach tries a serve.
- The simulator checks if it was good.
- If the serve was bad (hit the net), the coach learns why and tweaks the plan slightly.
- If the serve was good (high speed, lots of spin, perfect landing), the coach remembers that plan.
- Over time, the coach finds the "perfect" combination of speed, angle, and spin that a human couldn't easily calculate.

3. The "Secret Sauce": Dealing with the Wobble

One of the biggest challenges is the toss. When a human tosses a ball, it wobbles slightly. If a robot tries to hit a ball based on a "perfect" theoretical toss, it will miss because the real ball is slightly off.

The team solved this by teaching the robot to be robust. Instead of planning for one perfect toss, the AI tested thousands of slightly different wobbly tosses. It only kept the serve plans that worked even when the ball wobbled. This is like learning to ride a bike not just on a smooth road, but on a bumpy one, so you don't fall over when the road gets rough.

4. The Results: Beating the Pros

The team tested their robot against elite and professional human players (including Olympic medalists) in real tournaments with official referees.

Speed and Spin: The robot could spin the ball up to 550 radians per second and hit it at 6.7 meters per second. These numbers match or even beat the best human players.
Winning: The robot didn't just serve; it won points. In fact, as they improved the system, the robot's chance of winning a point when it served went up to nearly 59%, which is comparable to the best human pros.
The "Ace": The robot managed to hit "Aces" (serves the opponent couldn't return) at a rate of up to 21% in some matches.

5. Why This Matters (According to the Paper)

The paper claims this is the first time a robot has successfully generated official, rule-compliant, professional-level serves.

It proves that robots can handle the extreme physics of high-speed sports.
It shows that by combining smart math (optimization) with trial-and-error learning (Bayesian optimization), robots can do things that were previously thought too difficult because they require "explosive" but controlled movements.

In short, the team taught a robot to throw a ping-pong ball so perfectly that even the world's best players couldn't hit it back, using a mix of dance-like planning, crystal-ball simulation, and a very smart digital coach.

Technical Summary: "Ace! Motion Planning of Professional-Level Table Tennis Serves with a Robot Arm"

Problem Statement

While robotics research has extensively addressed the "rally" aspect of table tennis (returning incoming balls), the "serve" remains a significantly underexplored challenge. Unlike a return, where a robot leverages the incoming ball's momentum, a competitive serve requires generating high speed and/or high spin from a spinless, free-falling ball. This task presents extreme difficulties:

Physics Modeling: The robot must generate explosive but controlled motion to impart significant spin (up to 550 rad/s) and speed (up to 6.7 m/s) while adhering to International Table Tennis Federation (ITTF) rules.
Constraints: The ball must bounce first on the robot's side and then on the opponent's side, limiting the energy that can be applied. The racket must intercept the ball trajectory approximately perpendicularly, demanding higher precision than returning a ball.
Hardware Limitations: Mechanical actuators often lack the lightweight power and dexterity to replicate human wrist and arm movements, making motion planning for serves a complex optimization problem involving impact dynamics and body control.

Methodology

The authors present a comprehensive system combining motion primitives, Model Predictive Control (MPC), and Bayesian Optimization to generate ITTF-compliant, elite-level serve motion plans. The system utilizes an 8-DoF robot (gantry with 2 prismatic axes and a 6-DoF revolute arm) equipped with a racket featuring a ball cup for single-handed tossing.

1. Ball Toss (Motion Primitives)

The system employs a single-handed toss strategy, valid under ITTF rules.

Data Collection: Human demonstrations of one-arm tosses are collected and re-targeted to the robot's kinematics via optimization.
Execution: The robot executes a trajectory of joint commands ( $u_t(t)$ ) starting from a "flat" state.
Handling Stochasticity: Due to robot vibrations and environmental factors, the ball release point varies. The system empirically identifies the release time ( $t_{lift}$ ) using a ball triangulation system and averages trajectories using a Savitzky-Golay filter to account for noise.

2. Parametrized Motion Planner (MPC)

The striking motion ( $u_s(t)$ ) is generated by a non-linear hybrid optimization-based planner that solves for a minimum-jerk control sequence in both End-Effector (EE) and joint spaces.

Objective: Minimize squared jerk to ensure smooth, dynamically viable trajectories while satisfying constraints.
Constraints: The planner enforces initial/final joint state constraints and specific EE constraints at the contact time $\tau$ (position $p_\tau$ , normal $n_\tau$ , velocity $v_\tau$ ).
Soft Constraints: Terminal constraints for position, orientation, and velocity are softened using predefined physical tolerances (e.g., $\pm 5$ mm position, $\pm 0.5^\circ$ orientation) to accommodate high-speed tracking realities.
Solver: The problem is formulated as a chain of 32 piece-wise constant jerk polynomials and solved using the KNITRO solver, with typical solution times of 10–20 ms.

3. Parameter Optimization (HEBO)

Since analytical calculation of the optimal racket state ( $\xi_s$ ) is intractable due to non-linear ball dynamics and ITTF constraints, the authors use Heteroscedastic and Evolutionary Bayesian Optimization (HEBO).

Search Space: The optimizer searches over a normalized set of decision variables, including hit-timing, racket velocity, orientation (Euler angles), and return-to-rest duration.
Reward Function: The reward is a composite of terms evaluating:
- Legality ( $s_{leg}$ ): Sequential checks for ITTF compliance (e.g., correct bounce order, net clearance, no self-collision). Illegal serves receive hard penalties.
- Performance: Rewards for landing accuracy ( $r_{pos}$ ), velocity magnitude ( $r_{vel}$ ), height ( $r_{height}$ ), and specific spin components ( $r_{top/back}$ , $r_{side}$ ).
Robustness: To handle the stochastic nature of the toss, the optimizer evaluates candidates against multiple recorded toss trajectories, aggregating rewards to bias the search toward parameters robust to toss deviations.

4. Real-World Selection

A competition library is maintained and iteratively refined. Serves are selected for tournaments based on a heuristic algorithm that maximizes spin dissimilarity between consecutive serves to prevent opponents from adapting.

Key Results

The system was evaluated in tournaments against elite and professional Japanese table tennis players, officiated by licensed umpires.

Performance Metrics: The robot achieved serves with spins up to 550 rad/s and speeds up to 6.7 m/s, matching or surpassing elite human players.
Winning Probability: The robot maintained a point-winning probability while serving between 51.5% and 58.7% in April 2026, comparable to professional human benchmarks (approx. 52–53%).
Iterative Improvement: The paper details a progression from a baseline method (April 2025) to the final HEBO-based system (April 2026). Key improvements included:
- Incorporating multiple toss trajectories for robustness.
- Switching from a Genetic Algorithm to HEBO.
- Increasing dynamic limits (acceleration/jerk) to exploit full actuator capabilities.
- Strategic pruning of the serve library to remove serves that led to opponent points.
Task-Specific Generation: In controlled experiments, the system successfully generated serves with specific objectives (e.g., maximizing topspin, backspin, or sidespin), demonstrating a strong correlation between reward function weights and physical outcomes (e.g., generating -164 rad/s backspin when specifically rewarded).

Significance and Claims

The paper claims to present the first comprehensive system capable of generating professional-level, ITTF-compliant serve motion plans for a robot arm. Its significance lies in:

Bridging the Gap: Successfully addressing the "serve" problem, which requires pushing physics modeling and control to extremes, distinct from the rally problem.
Competitive Capability: Demonstrating that a robot can generate serves with velocity and spin comparable to or exceeding elite human players, contributing to a robot winning fair Best-of-3 matches against professional athletes for the first time.
Methodological Contribution: Proposing a framework that combines optimization-based motion planning with Bayesian Optimization (HEBO) to navigate complex, sparse, and noisy search spaces in robotics.

The authors acknowledge that the "sim-to-real" gap remains a challenge, noting that not all simulated motion plans transfer perfectly to hardware, and future work will focus on improved physics modeling and automatic fine-tuning on the hardware system.