Push the Limit: Learning High-Speed Sprinting and Aggressive Cornering on a Full-Scale Humanoid

Huaxing Huang; Ruidong Li; Jinchao Han; Ziyang Dong; Wenhao Cui

cs.ROOct 10, 2026

Push the Limit: Learning High-Speed Sprinting and Aggressive Cornering on a Full-Scale Humanoid

Authors: Huaxing Huang, Ruidong Li, Jinchao Han, Ziyang Dong, Wenhao Cui

Organizations: Noetix Robotics · Tsinghua University

Abstract

We present a learning-based framework that enables a full-scale bipedal humanoid to sprint at over 7 m/s with motion-prior-guided gait and perform aggressive cornering at high speed with a pronounced trunk lean of up to $25^\circ$ . Achieving this combination is challenging: above approximately 4 m/s, periodic foot impacts induce severe, high-frequency yaw-rate oscillations intrinsic to high-speed gaits. This high-frequency temporal structure corrupts the history of proprioceptive feedback that flat-MLP policies rely on, while rendering conventional yaw-rate tracking rewards counterproductive, as they fight against the robot's natural oscillatory dynamics. Moreover, a single style prior shared across skills cannot tell which skill is commanded and inherently compromises the low-speed skill fidelity. To overcome these limitations, we adopt a causal multi-head attention (MHA) module to explicitly model the high-frequency temporal feedback. In place of the oscillatory yaw rate, we design a heading-direction reward that supervises only the low-frequency velocity direction, allowing agile turning at high speed without suppressing natural gait oscillations. We further introduce skill-conditioned multi-adversarial-motion-prior (MAMP) discriminators that condition the style reward on the commanded skill. Ablation experiments confirm that each mechanism is essential: replacing structured temporal encoding with a flat-history MLP caps the top speed; reverting to yaw-rate tracking prevents high-speed turning; and a single shared discriminator makes in-place turning collapse into a quasi-static stance. Our framework bridges the gap between raw sprinting speed and reference-motion fidelity, demonstrating stable high-speed sprinting and aggressive cornering in both simulation and real-robot deployment.

Figures & tables

Figure 1: Gait sequences from simulation (Gazebo, rows 1 & 3) and real-robot deployment (rows 2 & 4). Rows 1–2: high-speed sprinting with motion-prior-guided stride dynamics at velocity command $6.5\,\mathrm{m/s}$ (timed hardware speed reported in Sec. ). Rows 3–4: aggressive cornering with maximum trunk lean exceeding $25^{\circ}$ at $5.5\,\mathrm{m/s}$ , an emergent inward-leaning strategy that arises from the heading-direction reward without explicit posture supervision.

Figure 2: System overview. (1) The MHA history encoder processes a $T$ -frame proprioceptive window via causal self-attention and fuses the dynamics summary with the current velocity-plus-skill command to produce joint position targets. (2) Skill-conditioned Multi-AMP discriminators provide an independent style reward per skill, conditioning the style reward on the commanded skill. (3) The heading-direction reward supervises the low-frequency velocity direction at high speed, falling back to yaw-rate tracking below $v_{\min}$ . All three components feed into a shared PPO training loop.

Figure 3: Encoder comparison in Gazebo (E1). (a) Step-test velocity tracking: MHA, GRU, LSTM, and HIM all track the $6.5\,\mathrm{m/s}$ command, generalizing beyond the $5.5\,\mathrm{m/s}$ training curriculum; the flat-history MLP saturates near $6.0\,\mathrm{m/s}$ . Curves smoothed with a $151$ -point moving average. (b) Cornering trajectories under command $(6.5,\,0,\,0.35)$ : MHA achieves a $24.2\,\mathrm{m}$ turning radius; LSTM and GRU require $1.8{\times}$ / $2.2{\times}$ larger radii; HIM falls. The green dashed circle marks the theoretical radius $r{=}v/|\omega|{=}18.6\,\mathrm{m}$ .

Figure 4: Turning-test comparison in Gazebo (E2 ablation). Both the heading-reward policy (ours, red) and the yaw-rate policy (E2 baseline, blue) receive the same command $(v_{x}{=}6.5\,\mathrm{m/s},\;\omega_{z}{=}0.35\,\mathrm{rad/s})$ ; theoretical radius $r{=}v/|\omega|{=}18.6\,\mathrm{m}$ . (a) World-frame XY trajectories over 15 laps. Thin transparent traces are raw trajectories; thick solid curves are least-squares fitted circles (Kasa method); the green dashed circle is the theoretical radius. Inset confirms both policies sustain ${\sim}6.5\,\mathrm{m/s}$ throughout. (b) Turning radius comparison: heading-reward $24.2\,\mathrm{m}$ ( $+30\%$ ) vs. yaw-rate $146.7\,\mathrm{m}$ ( $+690\%$ ). (c) Per-lap center drift: heading-reward $1.7{\pm}0.9\,\mathrm{m}$ vs. yaw-rate $8.2{\pm}2.7\,\mathrm{m}$ . (d, e) Cornering posture in Gazebo. The heading-reward policy leans $>13^{\circ}$ into the turn; the yaw-rate policy remains nearly upright.

	Stand	Turn	Walk	Run
Multi-AMP	$\mathbf{0.23}{\scriptstyle\pm.02}$	$\mathbf{2.62}{\scriptstyle\pm.01}$	$\mathbf{2.72}{\scriptstyle\pm.04}$	$\mathbf{4.64}{\scriptstyle\pm.03}$
Shared-D	$0.25{\scriptstyle\pm.01}$	$5.66{\scriptstyle\pm.04}$	$3.79{\scriptstyle\pm.01}$	$5.67{\scriptstyle\pm.07}$
Stand still	–	$5.76$	$6.95$	$14.34$

Table 1: E3 per-skill analysis in Isaac Lab (48 rollouts per skill). Left: DTW distance (

\downarrow

; mean per-frame L2 distance along the alignment, mean

\pm

s.d.); Stand still scores standing rollouts against each skill’s reference [ 5 ] . Right: style score

\rho(D)

of the in-place-turning discriminator of Multi-AMP (

D_{\mathrm{turn}}

) and of the shared discriminator (Sh.) on reference clips and on turning-command rollouts; compare within a row only, as Wasserstein scores are not calibrated across discriminators.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A.1: Timed $100\,\mathrm{m}$ hardware sprints on a standard athletics track. Top: primary platform (weight-reduced, same actuators and kinematics) completes $100\,\mathrm{m}$ in $14\,\mathrm{s}$ ( $7.14\,\mathrm{m/s}$ avg.) under a $7.0\,\mathrm{m/s}$ velocity command. Bottom: second humanoid ( $1.36\,\mathrm{m}$ , $40\,\mathrm{kg}$ , $23$ -DOF) completes $100\,\mathrm{m}$ in $22\,\mathrm{s}$ ( $4.55\,\mathrm{m/s}$ avg.) using the identical algorithmic framework.

Symbol	Description	Value
Robot
$h_{\mathrm{robot}}$	Robot standing height	$1.8\,\mathrm{m}$
Training (Sec. 3.5)
$f_{\mathrm{sim}}$	Physics simulation frequency	$200\,\mathrm{Hz}$
$n_{\mathrm{dec}}$	Control decimation	$4$
$f_{\mathrm{ctrl}}$	Policy control frequency ( $f_{\mathrm{sim}}/n_{\mathrm{dec}}$ )	$50\,\mathrm{Hz}$

Appendix

Table C.1: Symbols used in the main text and their numerical values.

PPO
Parameter	Value
Learning rate	$1\times 10^{-3}$ (adaptive schedule)
Discount $\gamma$	$0.99$
GAE $\lambda$	$0.95$
Clip parameter	$0.2$
Desired KL divergence	$0.01$

Appendix

Table C.2: PPO and discriminator training hyperparameters.

Component	Architecture	Params
History embed	MLP: $56\to 128\to 128$ (ELU)	$23{,}808$
Command embed	Linear: $7\to 128$	$1{,}024$
Positional encoding	Sinusoidal (non-learnable)	$0$
Causal Transformer	1 layer, 2 heads, $d{=}128$ , ff ${=}256$ , GELU, norm-first	$132{,}480$
History output LN	LayerNorm( $128$ )	$256$
Command fusion	Linear $256{\to}128$ + GELU + Linear $128{\to}128$	$49{,}408$

Appendix

Table D.1: MHA actor architecture. Total actor-side parameters:

471{,}970

Feature	Dimension
Joint positions	17
Key-point positions (selected body links)	54
Base linear velocity (XYZ)	3
Base angular velocity (RPY)	3
Joint velocities	17
Foot contact indicator	2

Appendix

Table D.2: AMP observation composition per frame.

Parameter	Range	Operation	Timing
Static / dynamic friction	$[0.3,1.0]$	Absolute	Startup
Restitution	$[0.0,0.5]$	Absolute	Startup
Joint default offset	$[-0.02,0.02]\,\mathrm{rad}$	Additive	Startup
Base COM offset (XYZ)	$\pm 0.05\,\mathrm{m}$	Additive	Startup
Base mass perturbation	$\pm 5.0\,\mathrm{kg}$	Additive	Startup
Actuator stiffness scale	$[0.8,1.2]\times$	Multiplicative	Each reset

Appendix

Table E.1: Domain randomization ranges.

Term	Description	Weight
Velocity Tracking
track_lin_vel_xy_exp	XY velocity tracking (exponential, $\sigma{=}0.5$ )	$5.0$
track_move_dir_to_heading_exp	Heading-direction alignment ( $\sigma{=}0.7$ )	$3.0$
track_lin_x_speed	Forward speed bonus	$2.0$
Base Regulation
flat_orientation_exp	Torso orientation ( $\sigma{=}0.5$ )	$1.0$

Appendix

Table E.2: Task reward function terms and weights.

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The pursuit of humanoid athletic sprints is hindered by a scarcity of humanoid-viable kinematic reference data and the inability of existing frameworks to maintain stability during sprints. To overcome these limitations, we introduce SPRINT, a novel framework driven by efficient, frequency-adaptive spectral priors. By characterizing the fundamental periodicity of human locomotion in the frequency domain using a reference library of five discrete motion sequences, these priors generate kinematically feasible joint trajectories across a broad velocity spectrum, successfully extrapolating to speeds that exceed the reference distribution. Guided by these pretrained priors, the SPRINT policy achieves zero-shot sim-to-real transfer in field experiments on the Unitree G1 platform, reaching a peak sprinting velocity of 6 m/s and demonstrating seamless gait transitions while preserving biomimetic naturalness. Ultimately, this work establishes frequency-adaptive spectral priors as a highly data-efficient foundation for humanoid athletic sprints. The project page is available at https://anonymous.4open.science/w/SPRINT-138A/.

Yantong Wei, Kaihong Huang, Hainan Pan +6

College of Intelligence Science and Technology, National University of Defense Technology, China · School of Artificial Intelligence and Robotics, Hunan University, China

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Apr 21, 2026

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Learning diverse locomotion skills for humanoid robots in a unified reinforcement learning framework remains challenging due to the conflicting requirements of stability and dynamic expressiveness across different gaits. We present a multi-gait learning approach that enables a humanoid robot to master five distinct gaits -- walking, goose-stepping, running, stair climbing, and jumping -- using a consistent policy structure, action space, and reward formulation. The key contribution is a selective Adversarial Motion Prior (AMP) strategy: AMP is applied to periodic, stability-critical gaits (walking, goose-stepping, stair climbing) where it accelerates convergence and suppresses erratic behavior, while being deliberately omitted for highly dynamic gaits (running, jumping) where its regularization would over-constrain the motion. Policies are trained via PPO with domain randomization in simulation and deployed on a physical 12-DOF humanoid robot through zero-shot sim-to-real transfer. Quantitative comparisons demonstrate that selective AMP outperforms a uniform AMP policy across all five gaits, achieving faster convergence, lower tracking error, and higher success rates on stability-focused gaits without sacrificing the agility required for dynamic ones.

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Jul 13, 2026

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A humanoid that can walk should not relearn locomotion from scratch to jog or run. Yet current approaches often obtain gait diversity by prescribing gait schedules, imitating motion clips, training experts to switch between or distilling skills into one policy. These strategies can produce impressive behaviors, but offer limited flexibility across continuous speed commands, terrains, and morphologies. We study skill growth with GaitSpan, a framework that expands a pretrained, basic walking policy into faster locomotion. It treats walking as a seed skill: reusable motor structure for balance, support, body coordination, and contact transition that can be regenerated at new rhythms, extended into longer/higher strides, and corrected by residual adaptation. This expansion has three aspects: 1) rhythm generation, which modulates the frozen walking policy with multiple internal clocks and learns command-conditioned combinations of the resulting canonical actions; 2) stride shaping, which rewards dynamic locomotion patterns appropriate for higher commanded speeds using a physically grounded objective inspired by spring-loaded inverted pendulum dynamics; and 3) residual adaptation, which captures motion details not accounted for by rhythm generation or stride shaping. GaitSpan is the first to deliver a single command-conditioned humanoid policy that spans walking, jogging, and running-like regimes covering a continuous speed range, transfers across morphologies, and deploys zero-shot on unseen sim-to-sim, and real-world terrains. Compared with baselines either trained with multi-experts or imitation from humans, it learns faster and achieves stronger gait performance.

Kwan-Yee Lin, Zilin Wang, Janelle J. Liu +1

University of Michigan · Skyline High School · University of Michigan, UC Berkeley

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