提出高效算法，让大规模机器人集群快速分布到目标密度，计算速度提升数十倍。
Computationally Efficient Density-Driven Optimal Control via Analytical KKT Reduction and Contractive MPC
- 通过解析降维将复杂优化问题简化为线性可扩展形式
- 在长时预测下计算时间从立方级降至线性级，实测提速超10倍
- 适用于无人机、机器人等需快速协同分布的场景
多智能体系统中高效协调空间分布是基础挑战。现有密度驱动最优控制（D2OC）框架能引导智能体轨迹匹配期望分布，但作为预测控制器需求解大规模卡尔希-库恩-塔克（KKT）系统，其计算复杂度随预测时长呈立方增长。为此，本文提出一种解析结构降维方法，将T步预测的KKT系统转化为紧凑型二次规划（QP），实现O(T)线性可扩展性，显著降低在线计算负担，相较传统O(T³)方法大幅提升效率。此外，为确保动态环境下的严格收敛性，引入收缩型李雅普诺夫约束，并证明闭环系统对参考漂移具有输入到状态稳定性（ISS）。数值仿真表明，该方法可在保证快速密度覆盖的同时实现显著计算加速，支持大规模多智能体集群的长时预测控制。
原文摘要 · Abstract (English)
Efficient coordination for collective spatial distribution is a fundamental challenge in multi-agent systems. Prior research on Density-Driven Optimal Control (D2OC) established a framework to match agent trajectories to a desired spatial distribution. However, implementing this as a predictive controller requires solving a large-scale Karush-Kuhn-Tucker (KKT) system, whose computational complexity grows cubically with the prediction horizon. To resolve this, we propose an analytical structural reduction that transforms the T-horizon KKT system into a condensed quadratic program (QP). This formulation achieves O(T) linear scalability, significantly reducing the online computational burden compared to conventional O(T^3) approaches. Furthermore, to ensure rigorous convergence in dynamic environments, we incorporate a contractive Lyapunov constraint and prove the Input-to-State Stability (ISS) of the closed-loop system against reference propagation drift. Numerical simulations verify that the proposed method facilitates rapid density coverage with substantial computational speed-up, enabling long-horizon predictive control for large-scale multi-agent swarms.
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