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

2026-09-17

AI Summary

本文提出了一种新的动力学松弛模型预测控制方法（DR-MPC）用于足式机器人运动，并开发了专门的内点法求解器，显著提高了计算速度。

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.

Problem

• model predictive control
• legged locomotion
• online optimization
• feasibility
• computation efficiency

Innovation

• dynamics-relaxed model predictive control
• interior-point method solver
• quadratic penalties
• block-arrow Hessian
• Schur complement