DR-MPC: Fast and Feasible Dynamics-Relaxed Model-Predictive Control for Legged Locomotion

Abstract:This paper presents dynamics-relaxed model predictive control (DR-MPC), a novel MPC formulation for legged locomotion, and a tailored interior-point method (IPM) solver. The formulation combines online optimization feasibility by construction with a contact-aware input parameterization. DR-MPC moves the dynamics equality and affine input constraints into quadratic penalties and retains only nonempty box constraints. The resulting box-constrained quadratic program (QP) has a block-arrow Hessian that enables the state and affine-output directions to be eliminated through a Schur complement. The solver factors only the reduced control system after swing-force elimination and contact-aligned move blocking. For the evaluated implementations using the same DR-MPC formulation, our method achieves median end-to-end MPC speedups of $16.0\times$ over HPIPM and $4.4\times$ over OSQP, with comparable locomotion performance in simulation. DR-MPC achieves a median onboard MPC end-to-end time of $4.4$ ms and is validated on a Unitree Go1 quadruped. Open-source code will be made available after publication.

Robotics (cs.RO); Systems and Control (eess.SY)

arXiv:2609.20035 [cs.RO]

(or arXiv:2609.20035v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.20035 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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