Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU
2026-04-08 • Robotics
RoboticsArtificial Intelligence
AI summaryⓘ
The authors developed GPU-SLS, a fast computer method that helps robots plan safe and robust movements in real-time, even when dealing with complicated robots and uncertain environments. They use a special way of solving math problems on a graphics processing unit (GPU) to speed up planning and control by a large margin compared to older methods. This technique keeps robots safe in practice and works on big systems like four-legged and humanoid robots, creating control plans in just milliseconds. Their code is also publicly available for others to use and build upon.
model predictive controlGPU accelerationnonlinear systemssequential quadratic programmingquadratic program solversystem level synthesisreachable setsrobust controlhigh-dimensional roboticsreal-time optimization
Authors
Jeffrey Fang, Glen Chou
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 237x. 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 x 10^5 decision variables and 8 x 10^4 constraints. The implementation of our method is available at https://github.com/Jeff300fang/gpu_sls.