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REVIEW 3 major objections 7 minor 27 references

Robot arm serves table tennis at pro level with 550 rad/s spin

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2026-07-09 22:04 UTC pith:TR3H24AW

load-bearing objection Letter re: Ace! Motion Planning of Professional-Level Table Tennis Serves the 3 major comments →

arxiv 2607.06989 v1 pith:TR3H24AW submitted 2026-07-08 cs.RO cs.SYeess.SY

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

Guillem Torrente , Guilherme Jorge Maeda , Divij Grover , Megumu Tsukamoto , Hamdi Sahloul , Peter D\"urr This is my paper
classification cs.RO cs.SYeess.SY
keywords servestabletenniscontrolmotionballoptimizationplanning
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper presents a framework for generating professional-level, rule-compliant table tennis serves using a robot arm. The core problem is that serving, unlike returning an incoming ball, requires generating high speed and spin from a stationary, spinless ball while obeying strict rules about bounce placement and net clearance. The authors solve this by decomposing the serve into three phases, preparation, toss, and strike, and optimizing the strike motion using a parametrized Model Predictive Controller whose parameters, the racket position, orientation, velocity, and timing at the moment of ball contact, are found via Bayesian Optimization. The optimizer explores the parameter space in simulation, penalizing illegal or unsafe motions and rewarding serves that match user-specified targets for spin type, landing location, and ball speed. The resulting motion plans are executed open-loop on the physical robot. The system achieves spins up to 550 rad/s and speeds up to 6.7 m/s, and was validated in competitive matches against professional players, where the robot's serve winning probability reached 51.5 to 58.7 percent, comparable to elite human performance.

Core claim

The central discovery is that the difficult, multi-objective problem of generating a legal, competitive table tennis serve, which requires simultaneously controlling ball spin, speed, landing position, and trajectory height from a spinless ball, can be decomposed into a fast parametrized motion planner whose key parameters are efficiently searched by a Bayesian optimizer in simulation. This combination produces motion plans that, when executed open-loop on real hardware, generate serves with spin and velocity matching or exceeding those of professional human players.

What carries the argument

The framework rests on three components. First, a parametrized motion planner solves a minimum-jerk optimization problem that drives the robot end-effector to a desired pose and velocity at a specified contact time, formulated as a chain of 32 piecewise-constant jerk polynomials with soft constraints on position, orientation, and velocity tolerances. Second, the Heterosceastic and Evolutionary Bayesian Optimization algorithm searches a normalized parameter space of up to ten variables defining the racket state at ball contact, using a Gaussian Process surrogate to efficiently explore a space dominated by infeasible solutions. Third, a reward function evaluates simulated serves through a casc

Load-bearing premise

The system assumes that motion plans optimized in simulation will transfer to the physical robot closely enough to produce competitive serves when executed open-loop, despite acknowledged sim-to-real gaps and stochastic ball toss variability that cannot be corrected in real time.

What would settle it

If the robot's serves, when executed open-loop on physical hardware, consistently failed to produce the spin, speed, or landing accuracy predicted by simulation, or if the serve winning probability against professional players were significantly below the 50 to 55 percent range typical of elite human servers, the core claim that the framework generates professional-level serves would be undermined.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The decomposition of a high-speed dynamic manipulation task into a parametrized planner plus black-box parameter search could generalize to other problems where the challenge lies in finding diverse motion profiles subject to quantifiable secondary objectives, such as throwing, catching, or striking tasks in sports or manufacturing.
  • The use of Bayesian optimization to handle stochastic ball tosses by evaluating candidate parameters across multiple sampled trajectories suggests a general approach for making open-loop robot execution robust to process noise without requiring real-time sensory feedback.
  • The competitive results against professional players suggest that, for certain sports tasks, open-loop execution of well-optimized motion plans can suffice, potentially reducing the need for expensive closed-loop perception and control systems in specific regimes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. This manuscript presents a framework for generating International Table Tennis Federation (ITTF)-compliant serve motion plans for a robot arm. The system combines a parametrized optimization-based motion planner (formulated as a minimum-jerk nonlinear program with soft terminal constraints), HEBO Bayesian optimization to search over racket strike parameters, and a sequential legality-checking pipeline. The motion planner generates joint-level commands that drive the racket end-effector to a desired pose and velocity at a specified contact time, while HEBO optimizes the serve type (spin, velocity, placement) by evaluating candidate parameters in simulation. The authors validate their approach through competitive matches against elite and professional players, including the Paris 2024 Olympic silver medalist, and report serve winning probabilities of 51.5–58.7%, comparable to professional baselines. The system achieves spins up to 550 rad/s and speeds up to 6.7 m/s.

Significance. The paper addresses a genuinely underexplored problem in robotics table tennis—the serve—as opposed to the extensively studied rally/return problem. The combination of MPC with Bayesian optimization for multi-objective serve generation is well-motivated, and the competitive validation against professional athletes, including umpire-officiated matches, is a notable strength that goes beyond typical simulation-only or laboratory-condition evaluations. The explicit ITTF compliance checking and the competition library management system add practical value. The framework's ability to generate diverse serve types (topspin, backspin, sidespin) with controllable characteristics, as shown in Table III, demonstrates the flexibility of the reward function design. The approach is a component of a system that reportedly won matches against professional players for the first time, which is a significant milestone. However, the significance of the peak performance claims is partially tempered by the lack of repeatability data for individual serves, as detailed in the major comments.

major comments (3)
  1. The abstract claims spins of up to 550 rad/s and speeds of up to 6.7 m/s, but these peak values are reported from a curated competition library rather than from controlled repeated trials of specific serves. Table III reports mean±std across different serves within a task category, not across repeated executions of the same serve. Given that the ball toss has approximately ±1 cm spread at contact time (Figure 3) and the strike is executed open-loop (Section III-C), the reproducibility of extreme-value serves is not established. The authors should report the distribution of outcomes (spin, velocity, landing position) for repeated executions of at least one representative high-spin and one high-velocity serve (e.g., 20 trials each), so that the reader can assess whether the peak values are reliably reproducible or one-off successes from a noisy distribution. This is load-bearing for the 's
  2. Section III-D and Table III: The sim-to-real transfer rate is approximately 50% (12–15 of 25 serves transfer zero-shot for each task). This suggests that the physics models underlying HEBO optimization are substantially approximate, yet the paper does not analyze which aspects of the sim-to-real gap are most impactful (e.g., ball-racket contact model, robot dynamics, ball toss variability). The authors acknowledge this gap in the Conclusions but do not quantify its effect on serve quality. A brief analysis of the failure modes for the non-transferred serves (e.g., did they fail legality checks, miss the table, or produce incorrect spin?) would strengthen the paper and help readers understand the limits of the approach.
  3. The match-winning probabilities in Table II (51.5–58.7% when serving) are comparable to the professional baseline of ~52–53% cited from [27]. While the authors frame this as achieving 'comparable effectiveness,' the data do not support a claim of surpassing elite players in match-level performance. The peak spin/velocity values may surpass human capabilities, but the match outcomes suggest competitive rather than dominant performance. The authors should clarify this distinction: the system surpasses elite players on peak physical metrics (spin, velocity) but achieves comparable match-level effectiveness. The current framing in the abstract ('matching and even surpassing those of elite table tennis players') conflates these two claims.
minor comments (7)
  1. Section III-C, Eq. (2): The polytopic set P is described abstractly as resulting from the dynamics model, kinodynamic limits, and polynomial sampling, but its specific construction is not detailed. A brief elaboration or reference to where P is defined would help reproducibility.
  2. Table I: The units for the slack weight ˆλn are listed as dimensionless (no unit), while ˆλp has units of m⁻¹ and ˆλv has units of (m/s)⁻¹. It would help to clarify how these weights interact in the objective (e.g., are the slack variables ϵp, ϵn, ϵv normalized before weighting, or are the weights set to balance the raw units?).
  3. Figure 4(b): The caption references subplots (b-1), (b-2), (b-3) but the content of each subplot is not clearly described. It would help to explicitly state what metric each subplot represents.
  4. Section III-D: The legality threshold percentage p (the fraction of sampled tosses that must pass legality checks) is mentioned but its value used in experiments is not reported.
  5. Section IV-A: The text states that 'later experiments were mostly conducted against professional players, whose level is higher than those of elite players,' but the distinction between 'elite' and 'professional' is not clearly defined. Clarifying this classification would help the reader interpret the match statistics.
  6. The paper references an earlier work [1] that employed 'an earlier version of this approach.' The relationship between the present manuscript and [1] should be clarified, particularly which components are novel versus inherited. The Contributions section states the motion planner and HEBO optimization as key components, but it is unclear whether these are entirely new relative to [1].
  7. Section III-B: The Savitzky-Golay filter parameters (window length, polynomial order) used to compute the average ball path are not specified.

Circularity Check

0 steps flagged

No circularity found; derivation chain is self-contained and validated against external benchmarks

full rationale

The paper's derivation chain is straightforward and non-circular. The motion planner (Eq. 2) is a standard constrained optimization producing jerk trajectories from physical parameters ξ_s. HEBO optimizes these physical parameters (racket velocity, orientation, timing) against a reward function (Eqs. 3-4) that measures independently verifiable physical quantities (ball spin, velocity, landing position) computed through physics simulation. No prediction reduces to a fitted input by construction. The reward terms decompose spin into physically meaningful components using a velocity-aligned frame, not a redefinition of the optimization variables. The self-citation to [1] (Dürr et al., Nature) is contextual ('an earlier version of this approach was employed') and not load-bearing for any mathematical claim—the full method is described independently here. Validation is against external benchmarks: ITTF rules, professional player serve data (Fig. 4), and competitive match outcomes (Table II). The ~50% sim-to-real transfer rate (Table III) is honestly reported and does not introduce circularity; it indicates model imperfection, not definitional equivalence. No step in the chain reduces to its own inputs.

Axiom & Free-Parameter Ledger

7 free parameters · 4 axioms · 0 invented entities

The paper introduces no new physical entities or forces. The free parameters are standard optimization hyperparameters (slack weights, tolerances, search bounds) and reward gains that are task-specific. The axioms are domain assumptions about the robot dynamics and simulation fidelity, which are standard in robotics but represent the main modeling simplifications.

free parameters (7)
  • MPC slack weights (lambda_p, lambda_n, lambda_v) = 2 m^-1, 1, 0.2 (m/s)^-1
    Hand-tuned weights for the soft constraint penalties in the motion planner objective (Table I).
  • MPC tolerances (Delta_p, Delta_phi, Delta_va, Delta_vr) = 5mm, 0.5deg, 0.01 m/s, 0.01
    Predefined physical tolerances for EE tracking error, chosen by the authors (Table I).
  • HEBO reward gains (g_back, g_top, g_side, d) = Task-dependent (e.g., g_back=1, g_top=0, g_side=1, d=-1)
    User-specified gains that select the desired spin profile for each serve type (Sec. III-D).
  • Position offset bounds (delta_p) = +/-0.07 m in each axis
    Bounded region for the optimizable racket position offset from the nominal ball trajectory.
  • Racket velocity bounds = [+/-10, +/-5, +/-5] m/s
    Physical bounds on the desired racket velocity at contact, set by the authors.
  • Legality threshold percentage p = Not specified numerically
    Percentage of sampled tosses that must pass legality checks for a genome to be deemed legal (Sec. III-D).
  • n_l (polynomial chain length) = 32
    Number of 3rd-degree polynomial segments for jerk parameterization, chosen to balance solver time and feasibility.
axioms (4)
  • domain assumption Joints can be modeled independently from each other in the dynamics model f_D.
    Sec. III-A states the second-order state-space model assumes all joints are independent, which is an approximation for a coupled 8-DoF system.
  • domain assumption The ball toss can be characterized by an average trajectory with bounded stochastic deviation.
    Sec. III-B and III-D assume the toss variability can be captured by sampling recorded trajectories and computing average rewards.
  • domain assumption The simulated physics models (ball-racket contact, aerodynamics, table bounce) are sufficiently accurate for HEBO to find transferable serves.
    The entire optimization pipeline runs in simulation; real-world execution is open-loop. The paper acknowledges sim-to-real gaps exist.
  • standard math Minimum-jerk trajectories are dynamically viable and produce smooth, safe robot motions.
    The MPC objective (Eq. 2) minimizes squared jerk, which is a standard smoothness criterion in motion planning.

pith-pipeline@v1.1.0-glm · 15530 in / 2600 out tokens · 302232 ms · 2026-07-09T22:04:37.879414+00:00 · methodology

0 comments
read the original abstract

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.

Figures

Figures reproduced from arXiv: 2607.06989 by Divij Grover, Guilherme Jorge Maeda, Guillem Torrente, Hamdi Sahloul, Megumu Tsukamoto, Peter D\"urr.

Figure 1
Figure 1. Figure 1: A high side-spin serve executed by the robot. The ball trajectory [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Our robot arm holding a ball on the ball cup, about to serve. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Real ball trajectories of serves used during the match against the Paris 2024 Olympic silver medalist Miu Hirano. (b) Ball velocities and heights as [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

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Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages · 1 internal anchor

  1. [1]

    Outplaying elite table tennis players with an autonomous robot,

    P. Dürret al., “Outplaying elite table tennis players with an autonomous robot,”Nature, vol. 652, no. 8111, pp. 886–891, Apr 2026

    work page 2026

  2. [2]

    "speed and spin characteristics of the 40mm table tennis ball

    H.-P. Tang, M. Mizoguchi, and S. Toyoshima, “"speed and spin characteristics of the 40mm table tennis ball",” Table tennis sciences, vol. 4, pp. 278–284, 2002

    work page 2002

  3. [3]

    Learn- ing to select and generalize striking movements in robot table tennis,

    K. Mülling, J. Kober, O. Kroemer, and J. Peters, “Learn- ing to select and generalize striking movements in robot table tennis,”The International Journal of Robotics Re- search, vol. 32, no. 3, pp. 263–279, 2013

    work page 2013

  4. [4]

    A robot ping-pong player: Experiment in real-time intelligent control,

    A. Russell, “A robot ping-pong player: Experiment in real-time intelligent control,” inAT Bell Laboratories. MIT Press, 1988

    work page 1988

  5. [5]

    Learning to play table tennis from scratch using muscular robots,

    D. Büchler, S. Guist, R. Calandra, V . Berenz, B. Schölkopf, and J. Peters, “Learning to play table tennis from scratch using muscular robots,”IEEE Transactions on Robotics, vol. 38, no. 6, pp. 3850–3860, 2022

    work page 2022

  6. [6]

    Achieving human level com- petitive robot table tennis,

    D. B. D’Ambrosioet al., “Achieving human level com- petitive robot table tennis,” in7th Robot Learning Work- shop: Towards Robots with Human-Level Abilities, 2025

    work page 2025

  7. [7]

    Learning strategies in table tennis using inverse reinforcement learning,

    K. Muelling, A. Boularias, B. Mohler, B. Schölkopf, and J. Peters, “Learning strategies in table tennis using inverse reinforcement learning,”Biological cybernetics, vol. 108, pp. 603–619, 2014. 8 TABLE III SERVE STATISTICS IN SIMULATION AND IN THE REAL WORLD FOR DIFFERENT TASK SETTINGS Task Environment Aim error [mm] Velocity [m/s] Spin [rad/s] x-y norm ...

    work page 2014

  8. [8]

    Robotic Table Tennis: A Case Study into a High Speed Learning System

    D. B. D’Ambrosioet al., “Robotic table tennis: A case study into a high speed learning system,”arXiv preprint arXiv:2309.03315, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  9. [9]

    The ping pong robot to return a ball precisely trajectory predic- tion and racket control for spinning balls,

    A. Kyohei, N. Masamune, and Y . Satoshi, “The ping pong robot to return a ball precisely trajectory predic- tion and racket control for spinning balls,” inOMRON Technics, vol. 51, no. 016, 2019

    work page 2019

  10. [10]

    Analysis of the spatial distribution of the serve and the type of serve-return in elite table tennis. Sex differences,

    F. Pradas, V . Toro-Román, C. Castellar, and L. Carrasco, “Analysis of the spatial distribution of the serve and the type of serve-return in elite table tennis. Sex differences,” Physical Education Theory and Methodology, 2023

    work page 2023

  11. [11]

    Serve analyses of elite european table tennis matches,

    Z. Djokic, “Serve analyses of elite european table tennis matches,”International Journal of Racket Sports Science, 01 2020

    work page 2020

  12. [12]

    Com- parison of rally time in xxix beijing (2008) and xxviii athens (2004) olympic table tennis tournaments,

    M. Katsikadelis, T. Pilianidis, and A. Misichroni, “Com- parison of rally time in xxix beijing (2008) and xxviii athens (2004) olympic table tennis tournaments,”Int. J. Table Tennis Sci, vol. 6, pp. 55–59, 2010

    work page 2008

  13. [13]

    International ta- ble tennis federation (ittf),

    International Table Tennis Federation, “International ta- ble tennis federation (ittf),” At: https://www.ittf.com, 2025

    work page 2025

  14. [14]

    Hebo: Pushing the limits of sample-efficient hyperparameter optimisation,

    A. Cowen-Riverset al., “Hebo: Pushing the limits of sample-efficient hyperparameter optimisation,”Journal of Artificial Intelligence Research, vol. 74, 07 2022

    work page 2022

  15. [15]

    Learning to serve: An experimen- tal study for a new learning from demonstrations frame- work,

    O. Koç and J. Peters, “Learning to serve: An experimen- tal study for a new learning from demonstrations frame- work,”IEEE Robotics and Automation Letters, vol. 4, no. 2, pp. 1784–1791, 2019

    work page 2019

  16. [16]

    Seal: A sample-efficient adjustment-learning method for table tennis robot serve,

    Q. Guo, X. Shi, K. Murakami, R. Jia, and Y . Yamakawa, “Seal: A sample-efficient adjustment-learning method for table tennis robot serve,” in2025 IEEE International Conference on Robotics and Automation (ICRA), 2025, pp. 14 924–14 930

    work page 2025

  17. [17]

    Ball trajectory planning in serving task for table tennis robot,

    Y . Hayakawa, A. Nakashima, S. Itoh, and Y . Nakai, “Ball trajectory planning in serving task for table tennis robot,” SICE Journal of Control, Measurement, and System Integration, vol. 9, pp. 50–59, 2016

    work page 2016

  18. [18]

    High speed robotic table tennis swinging using lightweight hardware with model predictive control,

    D. Nguyen, K. D. Cancio, and S. Kim, “High speed robotic table tennis swinging using lightweight hardware with model predictive control,” in2025 IEEE Interna- tional Conference on Robotics and Automation (ICRA), 2025, pp. 15 278–15 284

    work page 2025

  19. [19]

    Catching objects in flight,

    S. Kim, A. Shukla, and A. Billard, “Catching objects in flight,”IEEE Transactions on Robotics, vol. 30, no. 5, pp. 1049–1065, 2014

    work page 2014

  20. [20]

    Agile catching with whole-body mpc and blackbox policy learning,

    S. Abeyruwanet al., “Agile catching with whole-body mpc and blackbox policy learning,” inProceedings of The 5th Annual Learning for Dynamics and Control Con- ference, ser. Proceedings of Machine Learning Research, N. Matni, M. Morari, and G. J. Pappas, Eds., vol. 211. PMLR, 15–16 Jun 2023, pp. 851–863

    work page 2023

  21. [21]

    Learning-based design and control for quadrupedal robots with parallel-elastic actuators,

    F. Bjelonic, J. Lee, P. Arm, D. Sako, D. Tateo, J. Peters, and M. Hutter, “Learning-based design and control for quadrupedal robots with parallel-elastic actuators,”IEEE Robotics and Automation Letters, vol. 8, no. 3, pp. 1611– 1618, 2023

    work page 2023

  22. [22]

    Toward real-world automated anti- body design with combinatorial bayesian optimization,

    M. A. Khanet al., “Toward real-world automated anti- body design with combinatorial bayesian optimization,” Cell Reports Methods, vol. 3, no. 1, p. 100374, 2023

    work page 2023

  23. [23]

    Ac- quiring and generalizing the embodiment mapping from human observations to robot skills,

    G. Maeda, M. Ewerton, D. Koert, and J. Peters, “Ac- quiring and generalizing the embodiment mapping from human observations to robot skills,”IEEE Robotics and Automation Letters, vol. 1, no. 2, pp. 784–791, 2016

    work page 2016

  24. [24]

    Smoothing and differ- entiation of data by simplified least squares procedures

    A. Savitzky and M. J. E. Golay, “Smoothing and differ- entiation of data by simplified least squares procedures.” Analytical Chemistry, vol. 36, no. 8, pp. 1627–1639, 1964

    work page 1964

  25. [25]

    Coal: an extension of the flexible collision library,

    J. Pan, S. Chitta, D. Manocha, F. Lamiraux, J. Mirabel, J. Carpentier, L. Montautet al., “Coal: an extension of the flexible collision library,” https://github.com/coal- library/coal, 2015–2024

    work page 2015

  26. [26]

    R. H. Byrd, J. Nocedal, and R. A. Waltz,Knitro: An In- tegrated Package for Nonlinear Optimization, G. Di Pillo and M. Roma, Eds. Boston, MA: Springer US, 2006

    work page 2006

  27. [27]

    Analysis of contextual-related variables on serve and receiving performances in elite men’s and women’s table tennis players,

    M.-Á. Gómez, A. García-de Alcaráz, and P. Furley, “Analysis of contextual-related variables on serve and receiving performances in elite men’s and women’s table tennis players,”International Journal of Performance Analysis in Sport, vol. 17, no. 6, pp. 919–933, 2017

    work page 2017