DR-MPC: Fast and Feasible Dynamics-Relaxed Model-Predictive Control for Legged Locomotion
Authors: Run Wang, Alapati Tuerxun, Shuo Liu, Wei Xiao, Ján Drgoňa, Yilin Mo, Liang Wu
Organizations: Department of Automation, Tsinghua University, Beijing, China · Department of Mechanical Engineering, Boston University, Brookline, MA, USA · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore · Johns Hopkins University, Baltimore, MD 21218, USA
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× over HPIPM and 4.4× 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.