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

Model Predictive Control (MPC) delivers constraint-aware control, but its reliance on online optimization limits its use on systems with fast dynamics, high-dimensional models, or long horizons. Existing GPU implementations typically treat the device as a linear-algebra accelerator, leaving the optimization loop dependent on repeated kernel launches and high-latency memory transfers. This paper introduces CUDA MPC, a GPU-native MPC framework that co-designs the optimization algorithm, execution model, and memory architecture for CUDA hardware. CUDA MPC pairs a parallel-in-horizon alternating direction method of multipliers (ADMM) splitting with a fused CUDA kernel that runs the entire iterative solve on the device. Intermediate optimization variables stay in low-latency, on-chip shared memory, and a localized atomic-flag protocol synchronizes only adjacent horizon blocks, minimizing host intervention, kernel-dispatch overhead, and global-memory traffic. Across six nonlinear robotics benchmarks spanning increasing state dimension and constraint density, CUDA MPC sustains real-time rates at horizons one to two orders of magnitude longer than CPU solvers: it solves an optimization-based collision-avoidance parking problem with 100 s of lookahead within a 0.1 s sampling interval, and is the only solver evaluated that achieves both real-time execution and collision-free coordination for a centralized 10-agent swarm, where acados and CasADi return no feasible solution and require 3.5 s and 4.5 s per solve. Against tensor-framework implementations of the same ADMM splitting, the fused kernel is up to $965\times$ faster.

Real-time solution of nonlinear optimal control problems remains challenging on embedded robotic hardware, where conventional solvers often rely on global sparse linear algebra or sequential recursions that are difficult to map efficiently to massively parallel processors. This paper presents ucenter, a GPU-native Sequential Convex Programming (SCP) framework for nonlinear optimal control. At each SCP iteration, nonlinear dynamics are linearized around a nominal trajectory, and the resulting convexified subproblem is solved by a consensus Alternating Direction Method of Multipliers (ADMM) scheme. The temporal splitting replaces global sparse Karush-Kuhn-Tucker factorizations with independent per-node dense solves, closed-form dynamic consistency updates, and analytical projections onto convex constraint sets. Both the outer SCP loop and the inner ADMM subproblem are executed entirely on the GPU, enabling efficient optimization. The proposed solver is evaluated on quadrotor obstacle avoidance and Mars powered descent problems using an NVIDIA Jetson AGX Orin edge platform. Benchmarking against a CPU-parallel iLQR baseline in randomized environments reveals that the GPU implementation achieves over 100 Hz batched planning throughput, a 4.1x speedup, and a 51% reduction in energy consumption, while consistently maintaining low nonlinear dynamics defects. The framework exposes reusable GPU-parallel optimization primitives that can be specialized to a wide variety of complex nonlinear optimal control settings, as demonstrated by the scenario-based robust MPC and batched Monte Carlo generation tasks.

Robotics increasingly relies on GPUs for parallel simulation, large-scale learning, and neural-network inference. For model predictive control (MPC) to scale with this paradigm, solvers must run efficiently on this hardware while remaining fast, differentiable, and compatible with expressive MPC formulations used in robotics. We present TurboMPC, a differentiable MPC solver that runs entirely on the GPU and supports state and control inequality constraints, implicit integrators, cross-time-coupled costs, and slack variables. TurboMPC combines sequential quadratic programming (SQP), an alternating direction method of multipliers (ADMM) inner solver, implicit differentiation, and a co-designed JAX-CUDA implementation for efficiency and ease of use. In simulation, we validate TurboMPC on constrained planning, humanoid imitation learning, and reinforcement learning with neural-network cost function tasks, achieving up to $15\times$ and $58\times$ speedups over state-of-the-art CPU and GPU differentiable solvers, respectively. We deploy TurboMPC on a full-scale car for minimum-time racing and find that batched, GPU-accelerated tuning of MPC parameters via Bayesian optimization yields significantly faster driving than a hand-tuned baseline. TurboMPC also scales to planning horizons of over $8000$ knot points while maintaining control of the vehicle. We open-source TurboMPC at: https://github.com/ToyotaResearchInstitute/turbompc