Dynamics-Induced Commitment in Learning-Based Robotic Penalty Kicks

Humanoid kicking requires coordinated whole-body motion and precise contact, while a banana kick demands contact mechanics that generate ball spin and aerodynamic curvature. Motion imitation provides a reliable ordinary-kick prior, but reinforcement learning may improve shot speed and placement accuracy without changing the underlying kicking technique. Adapting this prior to a qualitatively different contact-rich skill can fail even when the reward is dense and optimization remains stable. The failure occurs when the task objective is locally flat over the current policy's responses. We term this condition first-order learning starvation. To address it, we propose response-informed skill evolution (RISE), a closed-loop objective-continuation method for policy adaptation. RISE ranks bounded objective changes using response sensitivity estimated from cached rollouts and accepts updates only when they produce verified response progress while preserving kicking reliability. Our analysis shows that rescaling a saturated spin reward cannot recover first-order sensitivity at zero spin, whereas adapting coupled contact responses can provide a learnable path to spin generation. We integrate RISE into a humanoid kicking pipeline under calibrated contact and Magnus-force aerodynamics, and sim-to-real transfer. Experiments show that RISE evolves the ordinary kick into a high-spin curved kick with 11.55 rad/s mean ball spin, improves the mean evaluation score by 19.8% over a learning-progress curriculum, and raises joint target attainment from 15.2% to 50.9%. Ablations and response diagnostics support the mechanism, while 30 motion-capture-recorded physical trials demonstrate consistent hardware transfer of the learned curved kick. Project website: https://haozhang-thu.github.io/bananakick/

Robots engaged in fast physical interactions often need to act before the intent of another agent is fully known. Anticipatory goalkeeping illustrates this challenge. Waiting provides more reliable information about the target but reduces the physical opportunity for interception, whereas acting early preserves reachability but requires initiating motion under uncertainty. Given a fixed closed-loop save controller, we formulate the decision of when to initiate motion as a policy-conditional finite-horizon optimal stopping problem. Building on this formulation, we propose monotone optimal stopping (MOS), a structured release-timing method for dynamic robotic interception. The quadruped save policy is trained with reinforcement learning, while MOS determines when the policy should be activated from the evolving robot state and target belief. Rather than predicting a release time or relying on confidence alone, MOS learns the return advantage of acting now over waiting for one more observation. We derive a direct Bellman recursion for this act-versus-wait margin and impose monotonicity only with respect to physical urgency, reflecting the irreversible loss of interception opportunity as time elapses. This structure enables early activation for dynamically demanding saves while preserving closed-loop adaptation when later observations change the predicted target. Under a single-crossing condition, MOS admits a threshold release boundary with a bounded approximation error. Extensive simulation studies show that MOS improves the mean save rate from 67.7% to 74.4% over a parameter-matched learned gate and increases reversal saves from 52.1% to 66.5%. Real-robot experiments further demonstrate rapid interception and post-release direction correction under human shot-direction feints.

Achieving human-level competitive intelligence and physical agility in humanoid robots remains a profound challenge, particularly in contact-rich and highly dynamic tasks such as boxing. While Multi-Agent Reinforcement Learning offers a principled framework for strategic interaction, its direct application to unstructured raw motor spaces inevitably leads to joint-level physical collapse, preventing the emergence of any viable combat tactics. To resolve this fundamental conflict between strategic exploration and physical feasibility, we formulate the humanoid combat task as a novel two-player latent-space zero-sum Markov game. Under standard regularity and approximate best-response assumptions, we show that the latent formulation induces an equivalent game over the decoder-reachable action manifold, providing an approximate-Nash interpretation of the resulting self-play dynamics. To instantiate this theoretical formulation, we propose RoboStriker, a hierarchical framework that decouples high-level reasoning from low-level execution. It first distills the tracking expertise of predefined boxing motions into a topologically bounded latent manifold. This structured latent foundation subsequently drives multi-agent co-evolution via Latent-Space Neural Fictitious Self-Play. Extensive experimental results demonstrate that gaming within this structured latent space substantially outperforms direct exploration. By constraining strategic exploration through a pretrained motion decoder, RoboStriker substantially reduces the catastrophic balance failures observed in raw action-space methods and achieves superior tactical performance in both competitive win rates and striking efficiency. Finally, we successfully deploy and validate our learned combat policies on real-world humanoid robots. Our code and video and supplementary materials are available at RoboStriker.