# 通过 GPU 上的可达性约束 System Level Synthesis 在毫秒级实现安全大规模鲁棒非线性 MPC

> 原文链接：https://robotics.hellobike.com/papers/2026-07-13-2604-07644
> 频道：papers | 更新日期：2026-07-13 | 标签：arxiv, cs.RO
> 核心摘要：提出 GPU-SLS，将可达性约束 SLS 与 GPU 并行 QP 用于安全鲁棒非线性 MPC，并在四足与人形等复杂系统上验证。

# 通过 GPU 上的可达性约束 System Level Synthesis 在毫秒级实现安全大规模鲁棒非线性 MPC

::: v-pre
> 原文链接：[Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://arxiv.org/abs/2604.07644)（arXiv 2604.07644 · 发布日期：2026-07-13）

**Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU**

提出 GPU-SLS，将可达性约束 SLS 与 GPU 并行 QP 用于安全鲁棒非线性 MPC，并在四足与人形等复杂系统上验证。

## 核心要点

- 面向高维不确定机器人系统和长规划时域，提升非线性 MPC 的安全性、鲁棒性与实时性。
- 联合优化满足不等式约束和动力学可行的名义轨迹、跟踪控制器及扰动下闭环可达集。
- 采用 GPU 加速 SQP/QP 求解器，并在 ADMM 中结合并行关联扫描和自适应缓存。
- 名义轨迹求解较 CPU 和 GPU 求解器分别减少 97.7% 与 71.8%，经验安全率达到 100%。

**验证范围与局限**：验证范围为复杂非线性系统，包括 61D 全身四足机器人和 75D 人形机器人。

## 英文摘要 (Abstract)

We present GPU-SLS, a GPU-parallelized framework for safe, robust nonlinear model predictive control (MPC) that scales to high-dimensional uncertain robotic systems and long planning horizons.Our method jointly optimizes an inequality-constrained, dynamically-feasible nominal trajectory, a tracking controller, and a closed-loop reachable set under disturbance, all in real-time.To efficiently compute nominal trajectories, we develop a sequential quadratic programming procedure with a novel GPU-accelerated quadratic program (QP) solver that uses parallel associative scans and adaptive caching within an alternating direction method of multipliers (ADMM) framework.The same GPU QP backend is used to optimize robust tracking controllers and closed-loop reachable sets via system level synthesis (SLS), enabling reachability-constrained control in both fixed-and receding-horizon settings.We achieve substantial performance gains, reducing nominal trajectory solve times by 97.7% relative to state-of-the-art CPU solvers and 71.8% compared to GPU solvers, while accelerating SLS-based control and reachability by 237→.Despite large problem scales, our method achieves 100% empirical safety, unlike high-dimensional learning-based reachability baselines.We validate our approach on complex nonlinear systems, including whole-body quadrupeds (61D) and humanoids (75D), synthesizing robust control policies online on the GPU in 20 milliseconds on average and scaling to problems with 2 → 10 5 decision variables and 8 → 10 4 constraints.

作者：Jeffrey Fang, Glen Chou
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## 原始参考来源 (Sources)

- [arXiv 2604.07644：Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://arxiv.org/abs/2604.07644)