基于对偶分解的分布式协同编队飞行研究

摘要

This paper presents a distributed algorithm to address the cooperative planning of multiple agents flying in formation. First, the cooperative trajectory planning subject to linear dynamics constraints is formulated as an op⁃timization problem, where the objective includes not only private (such as tracking reference trajectories) but also common (such as overall fuel consumption, formation and so on) goals for all agents. Second, in order to solve the optimization problem in a distributed fashion, the dual decomposition technique is employed to replace the original complex problem of very high computational load by multiple smaller sub⁃problems, which are then distributed over agents. Last but not least, a distributed algorithm is developed to solve the dual problem and thus the original coop⁃erative planning problem because there is no duality gap due to the convexity of the problem. Since the algorithm only requires neighbors′ information, it is scalable and applicable when the communication capabilities are limited. Simulation results show the efficiency and efficacy of the algorithm when applied to the cooperative planning of for⁃mation flying. Meanwhile, as compared with the centralized method, the optimality and convergence of the algorithm are demonstrated as well.%针对多智能体编队飞行问题，提出一种新的基于对偶分解的分布式算法，以实现协同航迹规划。首先，将编队飞行问题建模为受线性动力学约束的优化问题，其目标函数中包括智能体各自的独立目标（例如跟踪参考轨迹）以及系统的全局目标（例如总燃料消耗、编队队形等）。其次，为了分布式地求解该优化问题，将其对偶问题分解，把大计算量的原问题转化为多个小的子问题。最后，设计了协同分布式规划算法，并对其收敛性和最优性进行了理论证明。由于该算法只需相邻智能体间的通信，因此具有很强的可扩展性，并能适用于通信能力受限情况下的编队飞行。仿真结果表明，提出的分布式算法能有效地进行协同编队飞行规划；同时通过与集中式方法的比较，其最优性和收敛性得到了验证。