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.

Adversarial Motion Prior

See all 10 papers

SPRINT: Efficient Spectral Priors for Humanoid Athletic Sprints
May 27, 2026Yantong Wei, Kaihong Huang, Hainan Pan +6Humanoid Robot Locomotion Robot Motion Generation
College of Intelligence Science and Technology, National University of Defense Technology, China · School of Artificial Intelligence and Robotics, Hunan University, China
Multi-Gait Learning for Humanoid Robots Using Reinforcement Learning with Selective Adversarial Motion Prior
Apr 21, 2026Yuanye Wu, Keyi Wang, Linqi Ye +1Humanoid Robot Locomotion Adversarial Motion Prior
School of Future Technology, Shanghai University, Shanghai, 200444, China · National and Local Co-Built Humanoid Robotics Innovation Center, 201203 Shanghai, China
GaitSpan: Growing Humanoid Locomotion from Walking to Running
Jul 13, 2026Kwan-Yee Lin, Zilin Wang, Janelle J. Liu +1Humanoid Robot Locomotion Agent Skill Learning
University of Michigan · Skyline High School · University of Michigan, UC Berkeley

May 27, 2026J/K move · Enter open · S save

SPRINT: Efficient Spectral Priors for Humanoid Athletic Sprints

Yantong Wei, Kaihong Huang, Hainan Pan, Jiawei Luo+5

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

Humanoid Robot Locomotion Robot Motion Generation

Open paper AskPDF arXiv

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/.

Abstract

Adversarial Motion Prior

Explore similar work

SPRINT: Efficient Spectral Priors for Humanoid Athletic Sprints

Multi-Gait Learning for Humanoid Robots Using Reinforcement Learning with Selective Adversarial Motion Prior

GaitSpan: Growing Humanoid Locomotion from Walking to Running