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.

翻译：将交替方向乘子法（ADMM）与微分动态规划（DDP）相结合，为分布式多智能体轨迹优化提供了一个可扩展框架。实际应用中，为提升计算效率通常对ADMM进行截断，这导致原本分别控制协调质量与任务性能的参数紧密耦合。本文提出可微分协调（DiffCoord）——一个统一框架，针对截断ADMM-DDP流水线联合元学习这些耦合参数。参数由各智能体神经网络生成以适配任务，同构智能体共享相同网络，从而支持智能体数量动态变化。我们通过端到端微分ADMM-DDP流水线实现高效元学习，由此衍生出一个辅助的ADMM-LQR分布式梯度求解器，用于计算并协调这些参数的元梯度。该求解器继承了流水线的计算结构，可复用关键计算结果，并支持智能体间与轨迹时域的高效并行化。我们在协作式空中运输系统中通过数值与物理实验验证了DiffCoord，该系统可在狭小空间内重构四旋翼编队以实现安全的六自由度负载操控。该方法能鲁棒适应不同团队规模与负载动力学，且相较于最先进的轨迹梯度方法，将每个智能体的梯度计算时间降低高达70%。