Swarm trajectory optimization problems are a well-recognized class of multi-agent optimal control problems with strong nonlinearity. However, the heuristic nature of needing to set the final time for agents beforehand and the time-consuming limitation of the significant number of iterations prohibit the application of existing methods to large-scale swarm of Unmanned Aerial Vehicles (UAVs) in practice. In this paper, we propose a spatial-temporal trajectory optimization framework that accomplishes multi-UAV consensus based on the Alternating Direction Multiplier Method (ADMM) and uses Differential Dynamic Programming (DDP) for fast local planning of individual UAVs. The introduced framework is a two-level architecture that employs Parameterized DDP (PDDP) as the trajectory optimizer for each UAV, and ADMM to satisfy the local constraints and accomplish the spatial-temporal parameter consensus among all UAVs. This results in a fully distributed algorithm called Distributed Parameterized DDP (D-PDDP). In addition, an adaptive tuning criterion based on the spectral gradient method for the penalty parameter is proposed to reduce the number of algorithmic iterations. Several simulation examples are presented to verify the effectiveness of the proposed algorithm.

翻译：集群轨迹优化问题是一类公认的具有强非线性的多智能体最优控制问题。然而，现有方法需要预先设定智能体的终止时间这一启发式特性，以及大量迭代带来的耗时限制，阻碍了其在实践中应用于大规模无人机集群。本文提出一种时空轨迹优化框架，该框架基于交替方向乘子法实现多无人机共识，并利用微分动态规划进行单个无人机的快速局部规划。所引入的框架采用双层架构：使用参数化微分动态规划作为各无人机的轨迹优化器，并利用交替方向乘子法满足局部约束，实现所有无人机间的时空参数共识。由此得到一种完全分布式的算法，称为分布式参数化微分动态规划。此外，提出一种基于谱梯度法的惩罚参数自适应调整准则，以减少算法迭代次数。多个仿真算例验证了所提算法的有效性。