arXiv subjects

Gabriel Bravo-Palacios

Publications and source records attributed to Gabriel Bravo-Palacios.

4 recordsLinked to original sources

arXiv2026

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

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

cs.RO↗

arXiv2026

Parallel Dynamic Programming for Conic Linear Quadratic Control

Linear Quadratic (LQ) control problems are at the heart of linear control theory and Model Predictive Control (MPC). While performant, standard approaches to solving such problems are inherently serial, limiting real-time scalability despite the parallel computing power available on modern multi-core CPUs. Contributing to addressing this challenge and motivated by ``divide and conquer'' strategies, we present a parallel-in-time approach that solves computationally demanding conic optimal control problems through the use of the alternating direction method of multipliers (ADMM). In particular, we formulate the inner primal update of ADMM as an LQ problem and split the reformulated problem along the time horizon. This enables us to derive a variant of the Riccati recursion using dynamic programming to solve each subproblem in parallel. Numerical benchmarks on two real-world applications demonstrate as much as a 5x speedup compared to existing related approaches on multi-core CPU hardware.

math.OC↗

arXiv2026

TAG-K: Tail-Averaged Greedy Kaczmarz for Computationally Efficient and Performant Online Inertial Parameter Estimation

Accurate online inertial parameter estimation is essential for adaptive robotic control, enabling real-time adjustment to payload changes, environmental interactions, and system wear. Traditional methods often struggle to track abrupt parameter shifts or incur high computational costs, limiting their effectiveness in dynamic environments and for computationally constrained robotic systems. We introduce TAG-K, a lightweight extension of the Kaczmarz method that combines greedy randomized row selection for rapid convergence with tail averaging for robustness under noise and inconsistency. This design enables fast, stable parameter adaptation while retaining the low per-iteration complexity inherent to the Kaczmarz framework. We evaluate TAG-K in synthetic benchmarks and quadrotor tracking tasks against RLS, KF, and other Kaczmarz variants. TAG-K achieves 1.5x-1.9x faster solve times on laptop-class CPUs and 4.8x-20.7x faster solve times on embedded microcontrollers. More importantly, these speedups are paired with improved robustness to measurement noise and a 25% reduction in estimation error, leading to nearly 2x better end-to-end tracking performance. Website, documentation, and code available at: https://a2r-lab.org/TAG-K/.

cs.RO↗

arXiv2026

GATO: GPU-Accelerated and Batched Trajectory Optimization for Scalable Edge Model Predictive Control

While Model Predictive Control (MPC) delivers strong performance across robotics applications, solving the underlying (batches of) nonlinear trajectory optimization (TO) problems online remains computationally demanding. Existing GPU-accelerated approaches either parallelize single solves, handle large batches at sub-real-time rates, or sacrifice model generality for speed. This leaves a large gap in solver performance for many state-of-the-art MPC applications that require real-time batches of tens to low-hundreds of solves. As such, we present GATO, an open source, GPU-accelerated, batched TO solver co-designed across algorithm, software, and computational hardware to deliver real-time throughput for these moderate batch size regimes. Our approach leverages a combination of block-, warp-, and thread-level parallelism within and across solves for ultra-high performance. We demonstrate the effectiveness of our approach through a combination of: simulated benchmarks showing speedups of 18-21x over CPU baselines and 1.4-16x over GPU baselines as batch size increases; case studies highlighting improved disturbance rejection and convergence behavior; and finally a validation on hardware using an industrial manipulator. We open source GATO to support reproducibility and adoption.

cs.RO↗