A ZMP-Aware Task Formulation for Reference-Driven Humanoid Tracking in MuJoCo MPC

Reference-driven humanoid motion tracking aims to reproduce a source motion on a target humanoid while preserving physical executability under actuation limits and changing contact conditions. The problem becomes particularly challenging for dynamic motions involving rapid support transitions, landing impacts, mixed hand–foot contacts, and moderate topology-preserving morphology variation. Existing pipelines often rely heavily on morphology-specific world-frame targets or treat balance and contact quality only indirectly during execution, which limits their reliability under dynamic contact variation. This paper presents a task and cost formulation for reference-driven humanoid tracking within the residual-based MuJoCo model predictive control (MPC) framework. The source motion is decomposed into a pelvis-centered canonical local reference, pelvis height and tilt references, and a pelvis-derived horizontal center-of-mass (CoM) velocity intent, and is tracked online with a zero moment point (ZMP)-aware contact-conditioned residual design including slip, penetration, posture, and control regularization. The formulation is compatible with standard MuJoCo MPC planners, and the evaluation is conducted under a shared iterative linear quadratic Gaussian (iLQG) setting on nominal and morphology-varied humanoids against tracking-only and two-stage inverse-kinematics (IK)-based baselines. The proposed formulation improves success rate, support quality, slip reduction, and progression accuracy, with the clearest gains on contact-sensitive motions; for example, success rate increases from 56.7% to 76.7% on Jump–Turn and from 46.7% to 70.0% on Cartwheel relative to the tracking-only MPC baseline. These results support the use of execution-oriented reference representation and contact-conditioned residual design for physically reliable reference-driven humanoid tracking.