TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU
Authors: Gabriel Bravo-Palacios, Jianghan Zhang, Zachary Pestrikov, Brian Plancher, Thomas Lew
Abstract
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× and 58× 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
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× faster.
This paper introduces numerical optimizations for maximizing throughput on GPU when solving large batches (10,000 to over 100,000) of sequential quadratic programming (SQP) iterations, where all problems have the same structure. The optimizations are implemented in a toolbox WarpMPC for model-predictive control (MPC) in JAX and Warp. Based on the insight that all MPC problem instances in a batch share the same sparsity in time, cost, and constraints, we propose unrolling sparse linear factorizations and solves, which dominate alternating direction method of multipliers (ADMM) solver runtime. We avoid memory access bottlenecks and wasting computations via optimized memory layout, padding-reducing segmentation of the unrolled factorization, and dependency level scheduled backsolves, additionally accelerating sensitivity computation. We achieve throughputs of 8,000 to 250,000 SQP iterations per second on nonlinear cartpole, quadrotor, and humanoid robot benchmarks, outperforming baselines by 3× to 25×. We illustrate practical usefulness by synthesizing a dataset and training a neural network approximation of an MPC in under 4 minutes that stabilizes a nano quadrotor in hardware experiments.
In the literature, actor-critic model predictive control (AC-MPC) integrates MPC with reinforcement learning to enable high-performance control of complex dynamical systems. However, its differentiable MPC layer requires repeatedly solving an optimization problem in both the forward and backward passes, leading to substantial training and inference latency. This paper tackles this bottleneck introducing a CUDA-accelerated variant that significantly reduces end-to-end execution time while preserving the control performance of the baseline formulation. Simulation results on an agile drone racing task show that our approach achieves state-of-the-art lap times and near-limit dynamic behaviour with markedly reduced training and inference time.