Badminton is a compact but challenging domain for game AI: a player must choose a physically feasible shuttle trajectory, anticipate the opponent's interception, and recover to a court position whose value depends on the opponent's next response. The central challenge is that shot selection and recovery are not separable: the best recovery depends on the shot-induced opponent response, while the value of the shot depends on whether the hitter can cover the reply. This paper presents ShuttleArena, a physics-based singles badminton self-play environment that couples continuous shuttle flight, player interception, structured shot generation, and post-shot recovery. The policy uses role-conditioned outputs: a masked interception choice on receiver turns and a factorized hitter action over shot azimuth, shot elevation, shot speed, and recovery target, enabling interpretable tactical probes. Episodes are single rallies rather than full scored games, and training uses Proximal Policy Optimization (PPO) self-play against a staged checkpoint opponent pool with sparse terminal rally-outcome rewards and a factor-specific recovery update. Evaluation with frozen checkpoint play, controlled tactical probes, recovery ablations, qualitative rollouts, and a human-data sanity check shows competitive improvement together with interpretable opponent-conditioned changes in shot geometry and recovery behavior. The learned policies produce recognizable badminton-like structure while also reflecting the abstractions of the simulator, and the recovery intervention shows that learned recovery behavior is competitively important. These results suggest that physics-based racket sports are a useful testbed for interactive digital entertainment AI because they require agents to coordinate execution, positioning, and opponent-relative tactical value.
Figures & tables
Figure 1: Overview of ShuttleArena, including the state, role-conditioned policy, rally transition, and evaluation pipeline. The policy observes player positions, shuttle/contact features, feasible interception information, and rally context. On receiver turns it selects a feasible interception candidate; after contact, on hitter turns it factorizes the outgoing action into shot azimuth, elevation, speed, and recovery. The left panel compactly shows these consecutive decisions in one receive-and-return chain; they are not sampled jointly in one simulator step. ShuttleArena advances the rally through shuttle physics and opponent response, while PPO self-play trains against a checkpoint mixture and frozen checkpoints are evaluated by round-robin win-rate and rating analyses.
Component
Setting
Simulator
Singles court; 2D players; 3D shuttle flight with drag-square dynamics.
Movement
Speed 5.0 m/s; acceleration 8.0 m/s 2 ; racket length 1.6 m; reaction time 0.15 s.
Action space
Receiver: up to 20 masked interception candidates. Hitter: 11 azimuth ×8 elevation ×5 speed; 5×5 recovery grid.
Training
PPO self-play; 0 – 3.0 M pure-recency stage followed by 3.0 M– 6.0 M linear-recency continuation; 8 parallel environments.
Opponent pool
Stage 1: 6 checkpoint opponents with pure recency-biased sampling and 0.05 heuristic opponent probability. Stage 2: variety pool with 0.70 historical anchors sampled by linear recency, 0.15 recent continuation checkpoints, 0.05 newest continuation checkpoint, and 0.10 heuristic opponents.
Table 1: Key self-play configuration used for the models analyzed in this paper. Results are reported for checkpoints up to 6.0 M self-play timesteps.
Figure 2: Competitive evaluation across frozen checkpoints. (A) Illustrative single-lineage win-rate matrix where rows are evaluated checkpoints and columns are 30 fixed-pool opponents sampled every 0.2M timesteps from 0.2M to 6.0M; each cell uses 200 rallies. Off-diagonal patches show style-dependent matchups and possible non-transitivity. (B) Five-seed cross-fit Bradley–Terry/Elo comparison of pure-recency and pure+linear-recency training. Faint lines show individual seeds, thick lines show the mean, shaded bands show standard error, and the vertical line marks the 3.0M-step branch. The shared prefix and post-branch policies are connected through common fixed-pool opponents.
Figure 3: Controlled-contact trajectory samples across checkpoints. Each panel fixes a contact situation and overlays sampled 3D shuttle trajectories, with color indicating checkpoint step. The red star marks the fixed contact state, green markers show sampled landing choices, and the blue square marks the opponent position. Holding the contact state fixed makes changes in shot geometry and landing distribution visible across training.
Figure 4: Top-three shot trajectories for two fixed backcourt tactical states. The top row fixes a high left-backcourt contact while the opponent is positioned in the right backcourt; the bottom row fixes a high central-backcourt contact while the opponent starts in midcourt and moves laterally at 5m/s , indicated by the blue arrow. Each panel shows one high-probability shot mode; grayscale indicates action probability, the red marker shows the fixed contact location, the blue square shows the opponent position, and the black cross marks the projected landing point. The high-probability modes differ in landing depth, cross-court direction, speed, and trajectory geometry, showing how the policy conditions shot selection on opponent location and velocity.
Figure 5: Evolution of top recovery choices for fixed shot probes. The blue curve shows the fixed outgoing shot trajectory, the blue dot marks hitter contact, the red star marks expected opponent contact, and the dashed red curve shows a likely opponent response. Colored diamonds and triangles show the top and second recovery choices across checkpoints, revealing how recovery targets adapt to the same controlled tactical situation during training.
Figure 6: Sanity comparison between ShuttleArena policy rollouts and human singles rallies from ShuttleSet22. (A) Rally-length distributions across different seeds show that the learned policy produces shorter rallies than the human dataset. (B) Recovery targets are shallower, especially after net/drop, lift/clear, and smash/drive groups. (C) Landing distributions by contact zone are broadly similar in court regions, but the learned policy places more shots near sidelines and uses fewer net-contact lifts.
Figure 7: Recovery-choice intervention across five independent seeds. The shot policy is held fixed for each checkpoint, while the recovery factor is either the learned policy or a centered override. Lines show mean Elo-style ratings and shaded bands show standard error across seeds. The separation measures the total competitive consequence of replacing learned recovery, including the downstream state-distribution shift.
Figure 8: CRA/no-CRA training ablation for the main lineages. Checkpoints from the CRA and no-CRA lineages are evaluated against a common mixed fixed pool with 200 rallies per pair and summarized with one Bradley–Terry/Elo fit. Error bars show 95% bootstrap intervals obtained by resampling pair outcomes and refitting Elo. The CRA run is rated higher after early training in this evaluation.
Figure 9: Example ShuttleArena rallies rendered as stage-by-stage court snapshots. Each panel shows the active players, shuttle, outgoing flight path, intended intercept or landing point, and selected recovery target. The examples illustrate how ShuttleArena couples shot execution, receiver interception, and post-shot recovery across multi-stage exchanges with different terminal outcomes.
Hyperparameter
Value
Hidden layers
Policy/value MLP [64,64] ; factorized hitter heads; separate receiver head
Activation
Tanh
Learning rate
3×10−4
PPO clip ϵ
0.2
Discount γ
0.99
GAE λ
0.95
Table 2: Network and PPO hyperparameters for the primary analyzed self-play run. Values are from the run configuration or the Stable-Baselines3 defaults used when the training script does not override them.
Figure 10: Shuttle trajectory validation for four canonical shot families. Each panel shows the side-view ShuttleArena trajectory under the paper’s drag-square parameters ( kh=0.20 , kv=0.16 ). Shaded regions indicate external or canonical reference bands: the BWF correct-speed clear/lift landing window, close-to-net drop landing, Collet’s smash flight-time and speed-decay range, and a low drive net-crossing corridor. These checks are intended as plausibility validation of the shuttle-flight model, not as detailed calibration of player biomechanics or racket contact.
k scale
kh
kv
Half-dist.
VT
Clear short
Drop land
Smash t10
0.8
0.160
0.128
4.33
8.75
-1.69
2.57
0.304
0.9
0.180
0.144
3.85
8.25
-0.36
2.13
0.347
1.0
0.200
0.160
3.47
7.83
0.74
1.74
0.398
1.1
0.220
0.176
3.15
7.47
1.67
1.39
0.459
1.2
0.240
0.192
2.89
7.15
2.46
1.08
0.532
Table 3: Drag-robustness sweep for the validation shots. The same four launch examples are reused while scaling both drag coefficients. “Half-dist.” is the implied horizontal speed-halving distance ln2/kh ; VT is the implied vertical terminal speed g/kv . Clear shortfall is distance short of the far back line; negative values indicate that the fixed clear launch would travel long under reduced drag.
Variant
Change
Late beats early
Learned beats centered
CRA branch higher
Default
Original settings
Yes (0.865)
Yes (0.794)
Yes (0.721)
Lower drag
kh,kv−20%
Yes (0.540)
Yes (0.746)
Yes (0.780)
Higher drag
kh,kv+20%
Yes (0.781)
Yes (0.763)
Yes (0.860)
Slower player
Speed −15%
Yes (0.698)
Yes (0.805)
Yes (0.842)
Faster player
Speed +15%
Yes (0.868)
Yes (0.802)
Yes (0.673)
Longer reaction
Reaction time +50ms
Yes (0.603)
Yes (0.738)
Yes (0.714)
Table 4: Evaluation-time environment robustness for the main learned-policy conclusions. Policies are frozen and only the simulator constants are perturbed during evaluation. A “yes” means the first policy in the comparison exceeds a 0.5 rally win rate over 1000 side-balanced rallies, equivalent to five 200-rally evaluation pairs.
Figure 11: Aggregate controlled-probe action-space coverage and distribution shift. Shot statistics average over 27 fixed contact states from the controlled-contact grid; recovery statistics average over 81 fixed shot-response contexts from three recovery-start slices. Shaded bands show standard error across fixed states or contexts. Effective support is exp(H) for the empirical categorical distribution, and distribution shift is Jensen–Shannon divergence from the initial checkpoint. The shot policy changes substantially relative to initialization while remaining locally sparse, whereas recovery expands its effective grid support over training and remains far from the initial distribution.
We present ShuttleEnv, an interactive and data-driven simulation environment for badminton, designed to support reinforcement learning and strategic behavior analysis in fast-paced adversarial sports. The environment is grounded in elite-player match data and employs explicit probabilistic models to simulate rally-level dynamics, enabling realistic and interpretable agent-opponent interactions without relying on physics-based simulation. In this demonstration, we showcase multiple trained agents within ShuttleEnv and provide live, step-by-step visualization of badminton rallies, allowing attendees to explore different play styles, observe emergent strategies, and interactively analyze decision-making behaviors. ShuttleEnv serves as a reusable platform for research, visualization, and demonstration of intelligent agents in sports AI. Our ShuttleEnv demo video URL: https://drive.google.com/file/d/1hTR4P16U27H2O0-w316bR73pxE2ucczX/view
Ang Li, Xinyang Gong, Bozhou Chen +5
School of Computer Science, Peking University · Institute for Artificial Intelligence, Peking University
High-speed racket sports provide a demanding testbed for humanoid robots, requiring time-critical decisions, precise striking, and dynamic whole-body coordination. In badminton, fast-changing shuttle trajectories require timely contact decisions, while successful returns demand precise racket pose and velocity within a brief contact window and across a broad three-dimensional striking workspace. Human motion data provide valuable priors for such athletic skills, but usable badminton references are limited and imperfect. Direct tracking provides insufficient executable variation for diverse shuttle conditions, while purely task-driven optimization may produce unnatural motion. We therefore present a three-stage hierarchical reinforcement learning framework for dynamic humanoid badminton. First, task-randomized motion augmentation expands sparse annotated hitting events into executable target-conditioned stroke variations, forming a continuous latent skill space. Second, a high-level planner outputs continuous latent skill codes to compose these skills online according to the observed shuttle state. Third, a context-conditioned adversarial regularizer encourages more natural planner-level skill usage while preserving return performance. In real-world deployment, our system sustains multi-skill rallies with human players, including forehand, backhand, and highly dynamic jump returns. This is the first real-world humanoid racket-sport system to demonstrate multi-skill human--robot rallies including highly dynamic jump returns.
Jingzhi Cui, Zhexiong Wang, Bangjie Xu +9
Tsinghua University · Hong Kong Embodied AI Lab · Zhejiang University +3
Humanoid robots have demonstrated strong capabilities for interacting with static scenes across locomotion and manipulation, yet dynamic real-world interactions remain challenging. As a step toward fast-moving object interactions, we present an RL training pipeline that yields a unified whole-body controller for humanoid badminton, coordinating footwork and striking without motion priors or expert demonstrations. In badminton, locomotion and striking are tightly coupled, making the final hitting objective difficult to optimize directly due to sparse rewards and conflicting gradients. We address this with an annealed curriculum that first stabilizes learning through auxiliary locomotion objectives, then progressively removes them to focus optimization on the final hitting objective. For deployment, we use an Extended Kalman Filter (EKF) to estimate and predict shuttlecock trajectories for target striking, and also develop a prediction-free variant that removes the EKF and explicit prediction. We validate the framework in simulation and on hardware. In simulation, two robots sustain a rally of 21 consecutive hits. In real-world tests with both machine-fed shuttles and human-robot rallies, the robot achieves outgoing shuttle speeds up to 19.1 m/s. Moreover, the prediction-free variant attains comparable performance to the EKF-based policy. Overall, our approach enables dynamic yet precise goal striking in humanoid badminton and suggests a path toward more dynamics-critical whole-body interaction tasks.