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
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(−21∥vxy−vxycmd∥2/σvxy2)
16.0
Base ang vel tracking
exp(−21∥ωz−ωzcmd∥2/σωz2)
8.0
Locomotion
Standing contact
ρds21st
4.0
Step-period deviation
((αT−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 ( vxcmd ) and hopping commands ( hRF ). 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 ( vy ), and angular ( ωz ) velocity commands. Snapshots at 0.8 – 2.9s and at 7.6 – 10.8s 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 2.8m/s .
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.
Zewei Zhang, Kehan Wen, Michael Xu +7
Robotic Systems Lab, ETH Zurich · EPFL · Simon Fraser University +2
Despite recent advances in humanoid locomotion, controllers optimized for command tracking and robustness tend to produce mechanical gaits, whereas controllers tied to human motion data often fail to generalize to commands outside the data distribution. This work introduces a learning framework that balances these competing objectives to synthesize real-time steerable, robust, and biomimetic locomotion policies from human data. Using an in-house curated locomotion dataset covering diverse speeds and directions, we first learn a natural locomotion prior policy through a teacher-student distillation process. Specifically, we train a full-body reference-conditioned policy with Reinforcement Learning (RL), then distill it into a lightweight prior policy conditioned solely on proprioception and a planar torso-velocity steering command. Next, we fine-tune the prior policy with multi-task RL to expand command coverage and robustness beyond the data distribution, pairing a goal-conditioned task that tracks arbitrary commands with a reference-guided task that tracks the human data as an explicit style regularizer. We validate our framework on three humanoid robots: the Boston Dynamics Atlas R1, Atlas D1, and Unitree G1. Experimental results demonstrate robust performance across real-world scenarios, including direct user-controlled locomotion in indoor and outdoor environments, and integration as the locomotion layer within hierarchical control stacks. Benchmarks against Tabula Rasa RL policies trained without human data and ablation studies confirm that our framework yields a lightweight, deployable policy that reconstructs coordinated whole-body behavior from a steering command, retaining the human gait characteristics while remaining robust and fully steerable.
Mike Zhang, Dongho Kang, Kevin Bergamin +19
RAI Institute, USA · Boston Dynamics, USA · Carnegie Mellon University, USA
Human motion provides rich priors for training general-purpose humanoid control policies, but raw demonstrations are often incompatible with a robot's kinematics and dynamics, limiting their direct use. We present a two-stage pipeline for generating natural and dynamically feasible motion references from task-space human data. First, we convert human motion into a unified robot description format (URDF)-based skeleton representation and calibrate it to the target humanoid's dimensions. By aligning the underlying skeleton structure rather than heuristically modifying task-space targets, this step significantly reduces inverse kinematics error and tuning effort. Second, we refine the retargeted trajectories through progressive kinodynamic trajectory optimization (TO), solved in three stages: kinematic TO, inverse dynamics, and full kinodynamic TO, each warm-started from the previous solution. The final result yields dynamically consistent state trajectories and joint torque profiles, providing high-quality references for learning-based controllers. Together, skeleton calibration and kinodynamic TO enable the generation of natural, physically consistent motion references across diverse humanoid platforms.
Hanwen Wang, Qiayuan Liao, Bike Zhang +3
University of Wisconsin-Madison · University of California, Berkeley · Shanghai Innovation Institute (SII)