Brian Plancher

Sun, 23 Aug 2026 00:00:00 +0000

Parallel Dynamic Programming for Conic Linear Quadratic Control

Sun, 23 Aug 2026 00:00:00 +0000

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.

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

Tue, 23 Jun 2026 00:00:00 +0000

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 achieve up to 15x and 58x 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 scale to planning horizons of over 8000 knot points while maintaining control of the vehicle. We open-source TurboMPC at https://github.com/ToyotaResearchInstitute/turbompc

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

Mon, 01 Jun 2026 10:00:01 +0000

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.

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

Mon, 01 Jun 2026 00:00:00 +0000

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 resilience to measurement noise and a 25% reduction in estimation error, leading to nearly 2x better end-to-end tracking performance.