# DiffCoord: Differentiable Coordination for Distributed Multi-Agent Trajectory Optimization

arXiv: https://arxiv.org/abs/2509.01630 · HTML: https://mlsanity.com/paper/2509.01630/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 74 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Builds on (most cited first, 30 of 35)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Pontryagin Differentiable Programming: An End-to-End Learning and Control Framework](https://mlsanity.com/paper/1912.12970/) (2019)
- [DP-ADMM: ADMM-based Distributed Learning with Differential Privacy](https://mlsanity.com/paper/1808.10101/) (2018)
- [Safe Pontryagin Differentiable Programming](https://mlsanity.com/paper/2105.14937/) (2021)
- [Alternating Differentiation for Optimization Layers](https://mlsanity.com/paper/2210.01802/) (2022)
- [Optimal parameter selection for the alternating direction method of multipliers (ADMM): quadratic problems](https://mlsanity.com/paper/1306.2454/) (2013)
- [Efficient differentiable quadratic programming layers: an ADMM approach](https://mlsanity.com/paper/2112.07464/) (2021)
- [Actor-Critic Model Predictive Control: Differentiable Optimization meets Reinforcement Learning for Agile Flight](https://mlsanity.com/paper/2306.09852/) (2023)
- [Differentiable Linearized ADMM](https://mlsanity.com/paper/1905.06179/) (2019)
- [Control-oriented meta-learning](https://mlsanity.com/paper/2204.06716/) (2022)
- [Path Integral Networks: End-to-End Differentiable Optimal Control](https://mlsanity.com/paper/1706.09597/) (2017)
- [Deep Distributed Optimization for Large-Scale Quadratic Programming](https://mlsanity.com/paper/2412.12156/) (2024)
- [Constrained Differential Dynamic Programming: A primal-dual augmented Lagrangian approach](https://mlsanity.com/paper/2210.15409/) (2022)
- [Fast ADMM Algorithm for Distributed Optimization with Adaptive Penalty](https://mlsanity.com/paper/1506.08928/) (2015)
- [Agile and Cooperative Aerial Manipulation of a Cable-Suspended Load](https://mlsanity.com/paper/2501.18802/) (2025)
- [Adaptive Consensus ADMM for Distributed Optimization](https://mlsanity.com/paper/1706.02869/) (2017)
- [Distributed Differential Dynamic Programming Architectures for Large-Scale Multi-Agent Control](https://mlsanity.com/paper/2207.13255/) (2022)
- [Safety-Critical Coordination for Cooperative Legged Locomotion via Control Barrier Functions](https://mlsanity.com/paper/2303.13630/) (2023)
- [Differentiable Robust Model Predictive Control](https://mlsanity.com/paper/2308.08426/) (2023)
- [A Differentiable Augmented Lagrangian Method for Bilevel Nonlinear Optimization](https://mlsanity.com/paper/1902.03319/) (2019)
- [Online Control-Informed Learning](https://mlsanity.com/paper/2410.03924/) (2024)
- [Decentralized Aerial Manipulation of a Cable-Suspended Load using Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2508.01522/) (2025)
- [Constrained Differential Dynamic Programming Revisited](https://mlsanity.com/paper/2005.00985/) (2020)
- [Robust Multi-Robot Trajectory Optimization Using Alternating Direction Method of Multiplier](https://mlsanity.com/paper/2111.07016/) (2021)
- [RotorTM: A Flexible Simulator for Aerial Transportation and Manipulation](https://mlsanity.com/paper/2205.05140/) (2022)
- [Differentiable Optimal Control via Differential Dynamic Programming](https://mlsanity.com/paper/2209.01117/) (2022)
- [Nonlinear MPC for Full-Pose Manipulation of a Cable-Suspended Load using Multiple UAVs](https://mlsanity.com/paper/2301.08545/) (2023)
- [Kinodynamic Motion Planning for a Team of Multirotors Transporting a Cable-Suspended Payload in Cluttered Environments](https://mlsanity.com/paper/2310.03394/) (2023)

## Built on by (most cited first, 2 of 2)

- [Learning Multi-Agent Coordination via Sheaf-ADMM](https://mlsanity.com/paper/2605.31005/) (2026)
- [Autonomous Aerial Manipulation via Contextual Contrastive Meta Reinforcement Learning](https://mlsanity.com/paper/2606.08533/) (2026)

## Abstract (arXiv)

Integrating the Alternating Direction Method of Multipliers (ADMM) with Differential Dynamic Programming (DDP) provides a scalable framework for distributed multi-agent trajectory optimization. In practice, ADMM is typically truncated for computational efficiency, tightly coupling parameters that would otherwise separately govern coordination quality and task performance. In this paper, we propose Differentiable Coordination (DiffCoord), a unified framework that jointly meta-learns these coupled parameters for the truncated ADMM-DDP pipeline. These parameters are generated by agent-wise neural networks for task adaptation, and the same networks are shared among isomorphic agents to enable scalability to varying agent counts. We achieve efficient meta-learning by differentiating the ADMM-DDP pipeline end-to-end. Notably, this yields an auxiliary ADMM-LQR distributed gradient solver that computes and coordinates meta-gradients with respect to these parameters. This solver inherits the computational structure of the pipeline, enabling reuse of key computation results and efficient parallelization over agents and along trajectory horizons. We validate DiffCoord through numerical and physical experiments on a cooperative aerial transport system, where it reconfigures quadrotor formations for safe 6-DoF load manipulation in tight spaces. It adapts robustly to varying team sizes and load dynamics, while reducing per-agent gradient computation time by up to 70% compared with state-of-the-art trajectory-gradient methods.