Robotics Research Hub
Passive-Dynamic-Walking-Inspired Dynamics Guidance for Energy-Efficient Humanoid Locomotion

Passive-Dynamic-Walking-Inspired Dynamics Guidance for Energy-Efficient Humanoid Locomotion

Hyeonjin Choi, Joongheon Kim, Daekyum Kim · N/A · 2026

locomotion reinforcement-learning
PDF arXiv

Framework

N/A

License

N/A

Stars

N/A

Summary

Learning energy-efficient humanoid locomotion requires discovering mechanically economical gait coordination, not merely reducing actuator effort. Reinforcement learning promotes efficiency through effort-related reward penalties, which guide the step-to-step mechanics of walking only indirectly.

Abstract Summary

Learning energy-efficient humanoid locomotion requires discovering mechanically economical gait coordination, not merely reducing actuator effort. Reinforcement learning promotes efficiency through effort-related reward penalties, which guide the step-to-step mechanics of walking only indirectly. This article proposes a framework inspired by passive dynamic walking (PDW) that temporarily creates slope-equivalent conditions favorable to economical gait discovery and removes all PDW-specific guidance before nominal-dynamics optimization. During early training, a tilted-gravity field assists sagittal progression on flat collision geometry, complemented by curriculum-coupled reward terms. The core framework requires no reference trajectories, gait phases, or contact schedules. In a five-seed forward-locomotion study on a 29-DoF Unitree G1, the framework reduces mechanical cost of transport by 6.8-15.2% over commanded speeds of 0.5-2.0m/s without degrading velocity tracking. Mechanical-work decomposition attributes the reduction to positive actuator work, and reward-matched comparisons separate the guided regime's faster gait acquisition from the tilt's additional benefit to converged economy. The framework extends to unassisted omnidirectional locomotion, where its benefit persists once a walking-specific motion prior supplies kinematic coordination, the combination reducing speed-matched cost of transport by 18.7%. On hardware, forward cost of transport falls by 16.3% with the motion prior and by 4.5% without it, the latter within the trial-to-trial spread.

Key Points

  • Learning energy-efficient humanoid locomotion requires discovering mechanically economical gait coordination, not merely reducing actuator effort.
  • Reinforcement learning promotes efficiency through effort-related reward penalties, which guide the step-to-step mechanics of walking only indirectly.
  • This article proposes a framework inspired by passive dynamic walking (PDW) that temporarily creates slope-equivalent conditions favorable to economical gait discovery and removes all PDW-specific guidance before nominal-dynamics optimization.
  • During early training, a tilted-gravity field assists sagittal progression on flat collision geometry, complemented by curriculum-coupled reward terms.
  • The core framework requires no reference trajectories, gait phases, or contact schedules

Method

We consider flat-ground omnidirectional velocity tracking on an unmodified 29-DoF humanoid. The deployment task, policy interface, and baseline locomotion objective are identical across all comparisons.

The proposed PDW-inspired curriculum modifies early training through three coupled components: (i) command-conditioned virtual tilted gravity, (ii) curriculum-coupled PDW-inspired rewards, and (iii) a synchronized expansion from sagittally dominant to omnidirectional commands.

Method — Passive-Dynamic-Walking-Inspired Dynamics Guidance for Energy-Efficient Humanoid Locomotion
Fig. 3: Synchronized expansion of the translational command sectors and the yaw range over the curriculum. Left ($k Middle ($K_{w}\leq k Right ($k\geq K_{t}$): the union of the two sectors covers the full $360^{\circ}$ translational command range at the final yaw range. Green arrows denote admissible translational command directions; blue denotes the commanded yaw rate.

Experimental Setup

The robot is a 29-DoF Unitree G1. The nominal robot model has a mass of $m=33.34$ kg, which is used as the mass in all reported cost-of-transport values. Because this mass cancels in every relative comparison, the reported percentage reductions are invariant to its value. Training runs in Isaac Lab on Isaac Sim (PhysX) at a $50$ Hz control rate ($\Delta t=0.02$ s), with 1024 parallel environments and 20 s episodes.

Actions are 29 joint position targets tracked by implicit PD actuators.

Experimental Setup — Passive-Dynamic-Walking-Inspired Dynamics Guidance for Energy-Efficient Humanoid Locomotion
Fig. 4: Cost of transport on the sagittal task across commanded speeds (mean over 5 seeds; error bars show the S.D. of total CoT). Total bar height gives the total CoT, split into a positive component (dark) and a negative component (light). The full curriculum (Slope + VB + PW) attains the lowest CoT at every speed and lowers it primarily by shrinking the positive component, while the negative component stays essentially unchanged across all conditions and speeds.

Experimental Results

The experiments address four questions. First, does the proposed training scheme reduce mechanical cost of transport during forward locomotion without degrading command tracking? Second, is the reduction explained by lower positive actuator work, as intended by the reward design?

Third, do the VB-guided training regime and tilted-gravity assistance affect when sustained stepping first emerges during training, and is their effect on converged economy separable from that timing? Fourth, does the coordination developed under sagittal assistance ex...

Experimental Results — Passive-Dynamic-Walking-Inspired Dynamics Guidance for Energy-Efficient Humanoid Locomotion
Fig. 5: Emergence of sustained stepping during training (mean $\pm$ s.d. over five seeds). Left: mean foot-contact events per episode. Right: fraction of episodes with at least five step events. The horizontal axis is the PPO policy-update index. The flat and tilted-gravity variants with matched reward terms follow similar trajectories, whereas the conventional baseline reaches sustained stepping substantially later.

Sources and Demonstrations

Figures are reproduced from Choi et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.

Share

Related Papers

A Heterogeneous Architecture for Robot RL Beyond GPU-Dominant Paradigms
arXiv preprint

A Heterogeneous Architecture for Robot RL Beyond GPU-Dominant Paradigms

Yufei Jia, Zhanxiang Cao, Mingrui Yu et al.

Simulation-based RL for contemporary robot control is increasingly organized around GPU-resident simulation: physics, rollout collection, and learning are placed on a single GPU-centric execution path

reinforcement-learning simulation system-design locomotion
PDF Intermediate