发表机构
Tsinghua University; Boston University; Nanyang Technological University; Johns Hopkins University（清华大学; 波士顿大学; 南洋理工大学; 约翰斯·霍普金斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出DR-MPC，一种通过将动力学约束转为惩罚项并利用Schur补的高效MPC方法，在保持运动性能的同时，显著提升求解速度，并在四足机器人上验证。
AI 中文摘要
本文提出了动力学松弛模型预测控制（DR-MPC），一种用于腿部运动控制的新型MPC公式，以及一种定制的内点法（IPM）求解器。该公式通过构造将在线优化可行性与接触感知输入参数化相结合。DR-MPC将动力学等式和仿射输入约束转化为二次惩罚项，仅保留非空盒约束。由此产生的盒约束二次规划（QP）具有块箭形Hessian矩阵，可通过Schur补消除状态和仿射输出方向。求解器在摆动力消除和接触对齐移动阻塞后，仅对缩减的控制系统进行因式分解。对于使用相同DR-MPC公式的评估实现，我们的方法在仿真中实现了相对于HPIPM的中位端到端MPC加速16.0倍，相对于OSQP加速4.4倍，且运动性能相当。DR-MPC实现了4.4毫秒的中位机载MPC端到端时间，并在Unitree Go1四足机器人上得到验证。开源代码将在发表后提供。
英文摘要
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.
Comments8 pages, 5 figures, submitted to RA-L
