In the paper, we studied the continuous optimal control problem for multiagent pathfinding which is suitable for modelling various agents such as UAVs, swarms etc. Here, multiple agents try to find the best routes avoiding the obstacles and collisions. At first, we define path-traversing time cost functional. We show continuity of this functional and existence of the optimal path for a single agent. Then, we describe the multiagent pathfinding problem. Also, we consider game theory interpretation for the multiagent pathfinding with continuous routes and social behaviour. Various examples of optimal routes and agent behaviour strategies are provided.