FORGE: Feasible Online Reduced-Order Reference Generation and Whole-Body Execution for Agile Humanoid Locomotion

Adrian B. Ghansah; Yujin An; Jeeseop Kim; Soon-Jo Chung

cs.ROOct 27, 2026

FORGE: Feasible Online Reduced-Order Reference Generation and Whole-Body Execution for Agile Humanoid Locomotion

Authors: Adrian B. Ghansah, Yujin An, Jeeseop Kim, Soon-Jo Chung

Organizations: A. B. Ghansah, and S. J. Chung are with the Department of Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125, USA · Y. An is with the Department of Bioengineering, California Institute of Technology, Pasadena, CA 91125, USA · J. Kim is with the Dept. of Aerospace and Mechanical Engineering, The University of Texas at El Paso, TX 79968, USA

Abstract

This paper presents a two-stage learning framework for versatile and agile humanoid locomotion that couples online reduced-order model (ROM) reference generation with whole-body tracking control. In the first stage, we train a command-conditioned whole-body reference generator using single rigid body dynamics combined with full humanoid kinematics. In the second stage, the frozen ROM policy is rolled out online to generate references for training a whole-body tracking policy on the full-order dynamics model. Learning a kino-dynamically consistent reference generator in the simplified ROM space enables us to generate references over a broad command space and over multiple locomotion strategies using a single unified framework. We demonstrate the approach on a Unitree G1 humanoid robot, achieving longitudinal velocities from -2.0 m/s to 2.8 m/s, lateral velocities up to +-1.0 m/s, angular velocities up to +-3.0 rad/s, one-legged hopping, and continuous transitions across the commands, all using one unified reference policy and one whole-body tracking policy.

Figures & tables

Fig. 1 : A command generator drives the ROM controller and plant rollouts, from which we generate whole-body references that are passed to a whole-body tracking controller.

Fig. 2 : An overview of the two-stage training architecture. (Left) Illustrates the Stage 1 training, in which a command-conditioned whole-body reference generator is trained based on SRB dynamics and the full humanoid kinematics within a custom ROM simulator. (Right) Illustrates the Stage 2 training, in which a whole-body tracking policy for the full order system is trained to track the references generated in Stage 1.

Fig. 3 : (a) The different ROM foot contact modes. (b) The relationship between the swing foot phase and gait phase.

Reward Term	Expression	Weight
Task
Base lin vel tracking	$\exp\!(-\tfrac{1}{2}\lVert\mathbf{v}_{\textnormal{xy}}-\mathbf{v}^{\textnormal{cmd}}_{\textnormal{xy}}\rVert^{2}/\sigma_{v_{\textnormal{xy}}}^{2})$	$16.0$
Base ang vel tracking	$\exp\!(-\tfrac{1}{2}\lVert\omega_{\textnormal{z}}-\omega_{\textnormal{z}}^{\textnormal{cmd}}\rVert^{2}/\sigma_{\omega_{z}}^{2})$	$8.0$
Locomotion
Standing contact	$\rho_{\mathrm{ds}}^{2}\,1_{\mathrm{st}}$	$4.0$
Step-period deviation	$((\alpha_{T}-1)/0.4)^{2}$	$-2.5$

TABLE I : Reward terms used for ROM training.

Fig. 4 : The experiment shows how the ROM and FOM track time-varying longitudinal twist ( $v^{\mathrm{cmd}}_{x}$ ) and hopping commands ( $h_{\mathrm{RF}}$ ). It also illustrates the ROM motions, whole-body reference, and tracked FOM motions on the simulated robot.

Fig. 5 : Hardware experiments tracking time varying lateral ( $v_{y}$ ), and angular ( $\omega_{z}$ ) velocity commands. Snapshots at $0.8$ – $2.9~\mathrm{s}$ and at $7.6$ – $10.8~\mathrm{s}$ show the corresponding turning and lateral stepping motions, respectively.

Fig. 6 : Snapshots of hardware demonstrations: (a) Running on sloped uneven terrain. (b) One legged hopping on sand. (c) Running at $2.8~\mathrm{m/s}$ .

Humanoid Robot Locomotion

Humanoid robot locomotion studies how bipedal robots walk, run, recover from disturbances, and traverse varied terrain.

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Whole-body humanoid locomotion is challenging due to high-dimensional control, morphological instability, and the need for real-time adaptation to various terrains using onboard perception. Directly applying reinforcement learning (RL) with reward shaping to humanoid locomotion often leads to lower-body-dominated behaviors, whereas imitation-based RL can learn more coordinated whole-body skills but is typically limited to replaying reference motions without a mechanism to adapt them online from perception for terrain-aware locomotion. To address this gap, we propose a whole-body humanoid locomotion framework that combines skills learned from reference motions with terrain-aware adaptation. We first train a diffusion model on retargeted human motions for real-time prediction of terrain-aware reference motions. Concurrently, we train a whole-body reference tracker with RL using this motion data. To improve robustness under imperfectly generated references, we further fine-tune the tracker with a frozen motion generator in a closed-loop setting. The resulting system supports directional goal-reaching control with terrain-aware whole-body adaptation, and can be deployed on a Unitree G1 humanoid robot with onboard perception and computation. The hardware experiments demonstrate successful traversal over boxes, hurdles, stairs, and mixed terrain combinations. Quantitative results further show the benefits of incorporating online motion generation and fine-tuning the motion tracker for improved generalization and robustness.

Abstract

Humanoid Robot Locomotion

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