PMG: Parameterized Motion Generator for Human-like Locomotion Control

TL;DR

The paper introduces the Parameterized Motion Generator (PMG), a data-efficient framework for humanoid locomotion that produces natural, human-like motion under high-dimensional commands and VR teleoperation. It integrates Motion Preprocessing, Parameterized Gait Generation, and Ground-aware Command Optimization with an asymmetric imitation-RL training loop and a sim-to-real calibration pipeline, validated on the ZERITH Z1 platform. Key contributions include a compact, phase-based motion parameterization, an optimization step to enforce kinematic consistency, and a robust sim-to-real transfer strategy combining motor SysID, zero-point calibration, and domain randomization, plus real-world demonstrations in locomotion and teleoperation. Overall, PMG demonstrates high-fidelity, controllable locomotion and effective sim-to-real transfer, offering a practical pathway toward deployable humanoid control on non-commercial hardware.

Abstract

Recent advances in data-driven reinforcement learning and motion tracking have substantially improved humanoid locomotion, yet critical practical challenges remain. In particular, while low-level motion tracking and trajectory-following controllers are mature, whole-body reference-guided methods are difficult to adapt to higher-level command interfaces and diverse task contexts: they require large, high-quality datasets, are brittle across speed and pose regimes, and are sensitive to robot-specific calibration. To address these limitations, we propose the Parameterized Motion Generator (PMG), a real-time motion generator grounded in an analysis of human motion structure that synthesizes reference trajectories using only a compact set of parameterized motion data together with High-dimensional control commands. Combined with an imitation-learning pipeline and an optimization-based sim-to-real motor parameter identification module, we validate the complete approach on our humanoid prototype ZERITH Z1 and show that, within a single integrated system, PMG produces natural, human-like locomotion, responds precisely to high-dimensional control inputs-including VR-based teleoperation-and enables efficient, verifiable sim-to-real transfer. Together, these results establish a practical, experimentally validated pathway toward natural and deployable humanoid control.

Figures (4)

• Figure 1: Overview of the Parameterized Motion Generator (PMG). The framework comprises three stages: (a) Motion Preprocessing — raw mocap data(light bars) are retargeted to the robot and segmented into parameterized motion clips(darker bars). The database contains two types of clips: dynamic clips for locomotion, which are parameterized by phase $\phi\in[0,1)$, and static clips for posture adjustment, which are parameterized by their admissible command ranges. (b) Motion Generation — high-level commands are decomposed into a dynamic (velocity) command $\mathbf{u}_d$ and a static (posture) command $\mathbf{u}_s$. The dynamic and static modules generate respective reference trajectories, which are subsequently refined by a Ground-Aware Command Optimization module. (c) RL Training / Deployment — PMG outputs are incorporated into the observation and provided to the actor and critic; the actor's outputs are executed by low-level PD controllers and fed back to the environment.
• Figure 2: PMG motion comparison. All sequences are open-loop reference motions and have not been fine-tuned with reinforcement learning. (a–c) Reference clips from the robot dataset: (a) squatting from $D_{\mathrm{robot}}^{s}$, (b) forward-bend (pitch) from $D_{\mathrm{robot}}^{s}$, and (c) forward locomotion from $D_{\mathrm{robot}}^{d}$. (d–g) Synthesized motions: (d) synthesized motion without Ground-Aware Command Optimization (GCO); (e) the same sequence with red markers highlighting pronounced foot slip (physically inconsistent contact); (f) synthesized motion after applying GCO; (g) overlay showing that foot slip is substantially corrected.
• Figure 3: Real-world teleoperation experiments with the humanoid robot ZERITH Z1. (a) Wiping task: the robot moves a towel laterally across the tabletop for over $80 cm$. (b) Box-picking task: The robot lifts a black box (width $34\,\mathrm{cm}$) from a table of height $50\,\mathrm{cm}$, translates it horizontally by $\approx 60\,\mathrm{cm}$ to another table of height $76\,\mathrm{cm}$, and places it down.
• Figure 4: Tracking Curves Between Actual Joint Angles and Target Joint Angles Generated by Gait Generator.