TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU

2026-06-22

AI Summary

Traditional MPC solvers struggle to simultaneously achieve speed, differentiability, and support for complex constraints on GPUs, limiting their applicability to large-scale robotic systems. This work proposes TurboMPC—the first fully GPU-native, differentiable MPC solver capable of handling rich problem structures. By integrating SQP with an ADMM-based inner solver, TurboMPC supports state and control inequality constraints, implicit integration, temporally coupled costs, and slack variables. Leveraging a co-designed JAX-CUDA framework, it enables efficient automatic differentiation and massive parallelism. Experiments demonstrate that TurboMPC achieves 15× and 58× speedups over state-of-the-art CPU and GPU solvers in simulation, respectively. In real-world minimum-time autonomous racing, it significantly outperforms hand-tuned baselines and, for the first time, enables stable real-time control over horizons exceeding 8,000 nodes.

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 $15\times$ 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

Problem

• Model Predictive Control
• GPU acceleration
• Differentiable optimization
• Robotics
• Scalable control

Innovation

• differentiable MPC
• GPU acceleration
• sequential quadratic programming
• implicit differentiation
• JAX-CUDA