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arxiv: 2510.07625 · v2 · submitted 2025-10-08 · 💻 cs.RO · cs.SY· eess.SY

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

Alexander Du , Emre Adabag , Gabriel Bravo-Palacios , Brian Plancher This is my paper

Pith reviewed 2026-05-18 08:29 UTC · model grok-4.3

classification 💻 cs.RO cs.SYeess.SY
keywords GPU accelerationtrajectory optimizationmodel predictive controlbatched optimizationroboticsreal-time controledge computingnonlinear optimization
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The pith

GATO delivers real-time batched nonlinear trajectory optimization on GPU for moderate batch sizes in model predictive control.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents GATO as a GPU-accelerated solver for batches of nonlinear trajectory optimization problems that arise in model predictive control. It targets the regime of tens to low hundreds of simultaneous solves, where existing CPU methods are too slow and prior GPU methods either sacrifice speed or model generality. The core approach co-designs the algorithm, software stack, and hardware mapping to combine block-, warp-, and thread-level parallelism both within and across solves. This matters for robotics because many state-of-the-art MPC applications need multiple real-time solves for disturbance rejection and replanning on edge hardware. The authors demonstrate the result through scaling benchmarks, improved control behavior in case studies, and direct hardware validation on an industrial manipulator.

Core claim

GATO is an open-source GPU-accelerated batched trajectory optimization solver that combines block-, warp-, and thread-level parallelism to achieve real-time throughput for moderate batch sizes of nonlinear solves. It reports speedups of 18-21x over CPU baselines and 1.4-16x over other GPU baselines as batch size grows, together with better disturbance rejection and convergence, and is validated on physical hardware.

What carries the argument

Multi-level (block, warp, thread) parallelism applied within and across solves in a batched nonlinear trajectory optimization framework.

If this is right

  • Real-time model predictive control becomes practical on edge hardware for tasks that require simultaneous optimization of tens to low hundreds of trajectories.
  • Solver throughput improves with larger batch sizes, enabling better scalability in applications that benefit from multiple parallel plans.
  • Improved disturbance rejection and convergence rates are observed in simulated and hardware case studies.
  • The open-source release allows direct reproduction and integration into existing robotics control stacks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same multi-level parallelism strategy could be adapted to other batch optimization problems in robotics such as motion planning or parameter estimation.
  • Faster per-batch solve times may allow MPC to operate at higher replanning frequencies or with more complex dynamics models on the same hardware.
  • Energy use on embedded platforms could decrease because shorter computation windows leave more time in low-power states.

Load-bearing premise

That combining block-, warp-, and thread-level parallelism on the GPU produces no prohibitive synchronization costs and preserves generality for nonlinear problems at moderate batch sizes.

What would settle it

A benchmark run at batch sizes of 50-200 where GATO either falls below real-time rates, shows no speedup over a tuned CPU solver, or loses solution accuracy for the same nonlinear models.

Figures

Figures reproduced from arXiv: 2510.07625 by Alexander Du, Brian Plancher, Emre Adabag, Gabriel Bravo-Palacios.

Figure 1
Figure 1. Figure 1: The GATO solver parallelizes across batches of [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overall design of our batched solver which a) forms problems in parallel across solves and timesteps, b) leverages [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (Left) Solve times for 6-DoF manipulator motions while varying the batch size ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Average (normalized) merit function value across [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Figure-8 tracking task, with an external disturbance applied at the end effector. (Left) Bar chart shows tracking error, [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Simulation visualization at the last timestep of the [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Cumulative density function of the solve times for [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript presents GATO, an open-source GPU-accelerated batched trajectory optimization solver for model predictive control targeting moderate batch sizes of tens to low hundreds of solves. It claims to fill a performance gap by co-designing algorithm, software, and hardware with combined block-, warp-, and thread-level parallelism, reporting empirical speedups of 18-21x over CPU baselines and 1.4-16x over other GPU baselines, along with case studies on disturbance rejection and hardware validation on an industrial manipulator.

Significance. If the throughput claims hold with adequate analysis of overheads, the work would meaningfully advance real-time nonlinear MPC on edge hardware by supporting moderate batch regimes without sacrificing model generality. The open-sourcing for reproducibility and the inclusion of hardware experiments are clear strengths that enhance the practical value of the contribution.

major comments (1)
  1. Abstract: the central performance claims (18-21x CPU and 1.4-16x GPU speedups for moderate batch sizes) rest on the assumption that block-, warp-, and thread-level parallelism can be combined without prohibitive synchronization overhead or loss of generality for nonlinear TO. The abstract does not detail how data-dependent operations such as dynamics linearization or line search are scheduled to avoid warp divergence and cross-warp barriers in this batch-size regime, which is load-bearing for the real-time throughput assertion.
minor comments (2)
  1. The description of the GPU baselines would benefit from explicit statement of their batch-size scaling behavior and whether they also target moderate regimes, to strengthen the comparative claims.
  2. Consider adding a short table or paragraph summarizing the specific robot models, horizon lengths, and constraint types used in the simulated benchmarks to improve reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive review and for recognizing the practical value of GATO, including the open-source release and hardware validation. We address the single major comment below and outline a targeted revision to the manuscript.

read point-by-point responses

  1. Referee: Abstract: the central performance claims (18-21x CPU and 1.4-16x GPU speedups for moderate batch sizes) rest on the assumption that block-, warp-, and thread-level parallelism can be combined without prohibitive synchronization overhead or loss of generality for nonlinear TO. The abstract does not detail how data-dependent operations such as dynamics linearization or line search are scheduled to avoid warp divergence and cross-warp barriers in this batch-size regime, which is load-bearing for the real-time throughput assertion.

    Authors: We appreciate the referee highlighting the need for greater clarity on this point. The abstract is intentionally high-level to summarize the contribution and results. The detailed co-design of block-, warp-, and thread-level parallelism, along with the scheduling of data-dependent operations (dynamics linearization, line search, etc.) to control warp divergence and synchronization costs, is described in Sections 3 and 4 of the manuscript. Our implementation uses uniform batch processing, warp-level primitives for reductions, and kernel structures that minimize cross-warp barriers while preserving full nonlinear model generality. The reported speedups are measured end-to-end and already incorporate all overheads, as shown in the scaling benchmarks of Section 5. To make the abstract more self-contained and directly address the referee's concern, we will revise it to include a concise statement on the scheduling approach for data-dependent operations. revision: yes

Circularity Check

0 steps flagged

No significant circularity in empirical performance claims

full rationale

The paper presents GATO as an implemented co-designed GPU solver for batched nonlinear trajectory optimization and supports its real-time throughput claims exclusively through direct empirical benchmarks (speedups of 18-21x over CPU and 1.4-16x over other GPU baselines) plus hardware validation on an industrial manipulator. These are measured outcomes from simulated and physical tests rather than any derived predictions, first-principles results, or fitted parameters that reduce to the inputs by construction. No equations, uniqueness theorems, ansatzes, or self-citations are invoked as load-bearing steps in the provided claims; the central argument rests on the observed behavior of the block/warp/thread parallelism implementation itself, which is externally falsifiable via the open-sourced code and independent re-runs. The derivation chain is therefore self-contained in the engineering and benchmarking methodology.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions from nonlinear optimization and parallel computing literature; no new free parameters or invented entities are introduced beyond the software artifact itself.

axioms (1)
  • domain assumption Nonlinear trajectory optimization problems in MPC can be solved reliably with standard numerical methods when sufficient compute is available.
    Invoked implicitly when claiming real-time performance for general models.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Vectorizing Projection in Manifold-Constrained Motion Planning for Real-Time Whole-Body Control

    cs.RO 2026-04 conditional novelty 6.0

    Vectorizing projection operations enables real-time manifold-constrained motion planning for humanoid robots with 100-1000x speedups over prior methods.

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