Distributed cooperative planning of formation flying based on dual decomposition

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 optimization 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 cooperative 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 formation flying. Meanwhile, as compared with the centralized method, the optimality and convergence of the algorithm are demonstrated as well.