Path planning for multi-agent systems (MAS) is a challenging problem. This paper describes a novel method that utilizes particle swarm optimization to optimize trajectories of the leaders of a multi-quadcopter system (MQS) in a static and known environment. MQS collective motion in Rn (n = 1, 2, 3) is based on a leader-follower paradigm inspired by continuum mechanics. Under this paradigm, the MQS can deform under a homogeneous mapping. This homogeneous transformation in Rn is uniquely defined by the trajectories of n+1 leaders placed at the vertices of a deformable polytope called the leading polytope. With planned leader trajectories, the deformation can be acquired by the followers through local communication with n+1 nearby quadcopters. The proposed hierarchical path planning method consists of global path planning and local trajectory planning for MAS leaders. First, a collision-free roadmap, specifically a generalized Voronoi diagram, is generated. A well-established A* search procedure identifies an optimal route through this map. Waypoints on this optimal path are then passed into a particle swarm optimization (PSO) formulation that generates smooth trajectories for MQS leaders. The proposed method ensures collision avoidance and quadcopter containment. Simulation results demonstrate the proposed method.