Non-Robust MPC
Under disturbances, nominal rollouts can drift into obstacles because the plan does not account for closed-loop uncertainty.
Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU
Motivation
Fast nominal MPC can produce impressive trajectories, but disturbances can push the closed-loop system into unsafe states. GPU-SLS plans with robust reachable tubes so the controller has margin against uncertainty.
Robust MPC with Tubes
Reachable tubes tighten the constraints around the nominal plan, keeping all disturbed rollouts collision-free.
Method
GPU-SLS combines a GPU-parallel constrained SQP/ADMM trajectory optimizer with system level synthesis. The optimizer finds a dynamically feasible nominal trajectory, while SLS computes a disturbance-feedback controller and reachable tubes that certify robust constraint satisfaction.
GPU-SLS Overview
Parallel associative scans and cached factorizations make the trajectory, feedback, and reachability computations practical in a receding-horizon loop.
Results
Against DeepReach, GPU-SLS explicitly synthesizes a robust feedback policy and reachable tube online, avoiding the unsafe rollouts produced by the learned safety certificate.
DeepReach
DeepReach fails to consistently certify safety under adversarial and random disturbance.
GPU-SLS
Our reachable-tube controller keeps the rollouts safe across the same obstacle-avoidance setting.
Long-Range Dubins Navigation
GPU-SLS synthesizes robust policies for long-range fields with many obstacle constraints, maintaining safety over extended horizons.
The same formulation scales from low-dimensional planning benchmarks to whole-body humanoid systems, where the policy must account for high-dimensional dynamics and uncertainty.
Robust SLS Humanoid Rollouts
Disturbed humanoid rollouts remain inside the synthesized robust tubes.
Robust MPC Humanoid
Reachability-constrained MPC enables high-dimensional humanoid navigation around obstacles.
Finally, GPU-SLS runs on real quadruped hardware, producing robust whole-body control policies that navigate around obstacles in real time.
Real-Time Robust MPC and SLS
Robust whole-body control on quadruped hardware with online tube-aware policy synthesis.
Hardware Quadruped
Whole-body constrained MPC on a Unitree Go2 hardware platform.
Collision Margin
The hardware rollout maintains positive distance to obstacles while tracking the robust plan.
BibTeX
View TeX@article{fang2026gpu_sls,
title={Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU},
author={Fang, Jeffrey and Chou, Glen},
institution={Georgia Institute of Technology},
year={2026}
}