# Transformer-based Model Predictive Control: Trajectory Optimization via Sequence Modeling

arXiv: https://arxiv.org/abs/2410.23916 · HTML: https://mlsanity.com/paper/2410.23916/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 31 Oct 2024.

## Builds on (most cited first, 16 of 16)

- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [Offline Reinforcement Learning as One Big Sequence Modeling Problem](https://mlsanity.com/paper/2106.02039/) (2021)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Toward the Fundamental Limits of Imitation Learning](https://mlsanity.com/paper/2009.05990/) (2020)
- [Learning Sampling Distributions for Robot Motion Planning](https://mlsanity.com/paper/1709.05448/) (2017)
- [On the Convergence and Sample Efficiency of Variance-Reduced Policy Gradient Method](https://mlsanity.com/paper/2102.08607/) (2021)
- [Variance Reduction for Policy Gradient with Action-Dependent Factorized Baselines](https://mlsanity.com/paper/1803.07246/) (2018)
- [Combining Optimal Control and Learning for Visual Navigation in Novel Environments](https://mlsanity.com/paper/1903.02531/) (2019)
- [Large Scale Model Predictive Control with Neural Networks and Primal Active Sets](https://mlsanity.com/paper/1910.10835/) (2019)
- [Robotic Table Wiping via Reinforcement Learning and Whole-body Trajectory Optimization](https://mlsanity.com/paper/2210.10865/) (2022)
- [Learning Mixed-Integer Convex Optimization Strategies for Robot Planning and Control](https://mlsanity.com/paper/2004.03736/) (2020)
- [Model Predictive Control for Micro Aerial Vehicles: A Survey](https://mlsanity.com/paper/2011.11104/) (2020)
- [Advances in Trajectory Optimization for Space Vehicle Control](https://mlsanity.com/paper/2108.02335/) (2021)

## Built on by (most cited first, 16 of 16)

- [Warm-Starting Optimization-Based Motion Planning for Robotic Manipulators via Point Cloud-Conditioned Flow Matching](https://mlsanity.com/paper/2510.03460/) (2025)
- [Agile Tradespace Exploration for Space Rendezvous Mission Design via Transformers](https://mlsanity.com/paper/2510.03544/) (2025)
- [Tiny Recursive Control: Iterative Reasoning for Efficient Optimal Control](https://mlsanity.com/paper/2512.16824/) (2025)
- [Language-Conditioned Safe Trajectory Generation for Spacecraft Rendezvous](https://mlsanity.com/paper/2512.09111/) (2025)
- [Learning to accelerate Krasnosel'skii-Mann fixed-point iterations with guarantees](https://mlsanity.com/paper/2601.07665/) (2026)
- [Receding-Horizon Control via Drifting Models](https://mlsanity.com/paper/2604.04528/) (2026)
- [Transformer-Based Warm-Starting for Feasible and Optimal Terminal Approach to Tumbling Objects with Space Manipulators](https://mlsanity.com/paper/2606.17317/) (2026)
- [Learning Robust Satellite Attitude Dynamics with Physics-Informed Normalising Flow](https://mlsanity.com/paper/2508.07841/) (2025)
- [Flow-Opt: Scalable Centralized Multi-Robot Trajectory Optimization with Flow Matching and Differentiable Optimization](https://mlsanity.com/paper/2510.09204/) (2025)
- [Hybrid Model Predictive Control with Physics-Informed Neural Network for Satellite Attitude Control](https://mlsanity.com/paper/2602.15954/) (2026)
- [Safety-Guaranteed Imitation Learning from Nonlinear Model Predictive Control for Spacecraft Close Proximity Operations](https://mlsanity.com/paper/2603.18910/) (2026)
- [Tiny Recursive Models for Solving the J2-Perturbed Lambert Problem](https://mlsanity.com/paper/2606.00895/) (2026)
- [HOLO-MPPI: Multi-Scenario Motion Planning via Hierarchical Policy Optimization](https://mlsanity.com/paper/2606.16480/) (2026)
- [Guided Riemannian Optimization (GuRO): Bridging Model Predictive Control and Decision Transformers](https://mlsanity.com/paper/2608.23204/) (2026)
- [Transformer-Informed Trajectory Optimization for Relative Motion in Cislunar Orbits](https://mlsanity.com/paper/2609.25460/) (2026)
- [RL-Guided PAC-NMPC for Probabilistically-Safe Perception-Based Navigation in Unknown Environments](https://mlsanity.com/paper/2609.39854/) (2026)

## Abstract (arXiv)

Model predictive control (MPC) has established itself as the primary methodology for constrained control, enabling general-purpose robot autonomy in diverse real-world scenarios. However, for most problems of interest, MPC relies on the recursive solution of highly non-convex trajectory optimization problems, leading to high computational complexity and strong dependency on initialization. In this work, we present a unified framework to combine the main strengths of optimization-based and learning-based methods for MPC. Our approach entails embedding high-capacity, transformer-based neural network models within the optimization process for trajectory generation, whereby the transformer provides a near-optimal initial guess, or target plan, to a non-convex optimization problem. Our experiments, performed in simulation and the real world onboard a free flyer platform, demonstrate the capabilities of our framework to improve MPC convergence and runtime. Compared to purely optimization-based approaches, results show that our approach can improve trajectory generation performance by up to 75%, reduce the number of solver iterations by up to 45%, and improve overall MPC runtime by 7x without loss in performance.