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

A new differentiable model predictive control solver called TurboMPC runs entirely on a GPU and delivers speedups of up to 58 times over existing GPU-based differentiable solvers, according to a paper posted to arXiv by researchers at the Toyota Research Institute [1]. The solver, detailed in a preprint submitted on June 23, 2026, combines sequential quadratic programming with an alternating direction method of multipliers inner solver, implicit differentiation, and a co-designed JAX-CUDA implementation [1]. It supports state and control inequality constraints, implicit integrators, cross-time-coupled costs, and slack variables — features the authors describe as necessary for expressive MPC formulations in robotics [1]. In simulation benchmarks, TurboMPC achieved speedups of up to 15× over state-of-the-art CPU differentiable solvers and up to 58× over GPU differentiable solvers [1]. The paper validates the approach on constrained planning, humanoid imitation learning, and reinforcement learning tasks that use neural-network cost functions [1]. The work arrives as robotics pipelines increasingly shift computation onto GPUs for parallel simulation, large-scale learning, and neural-network inference [2]. A related effort, DiffMPC, previously tackled the same bottleneck by introducing a GPU-accelerated differentiable optimization tool that uses a preconditioned conjugate gradient routine with tridiagonal preconditioning to exploit the structure of optimal control problems [5]. That solver demonstrated speedups on reinforcement learning and imitation learning benchmarks and was tested on a Toyota Supra performing robust drifting through water puddles [5]. TurboMPC’s inner quadratic programs are solved by a custom ADMM scheme inspired by the OSQP solver, with primal-update linear systems handled via the cuDSS library [3]. The authors use implicit differentiation and custom vector-Jacobian products to obtain gradients through the active-set KKT conditions, avoiding the need to expand the problem size for slack variables [3]. The researchers deployed TurboMPC on a full-scale car for minimum-time racing. Batched, GPU-accelerated tuning of MPC parameters via Bayesian optimization produced significantly faster lap times than a hand-tuned baseline [1]. The solver also scaled to planning horizons exceeding 8,000 knot points while maintaining vehicle control [1]. The code has been open-sourced under the Toyota Research Institute’s GitHub organization [1]. Gabriel Bravo Palacios is listed as the corresponding author on the submission [1].