Several control problems have been solved for multi-agent systems, especially with respect to control and stabilization of formations. Often, hybrid system models are used to describe changing communication protocols and decision making in this context. Nevertheless, there is still not much focus on the performance of task execution.

Here, optimal planning for a transportation task that involves multiple vehicles is considered. Paths for the vehicles are sought such that an object is transported from a start to a goal position. Several of the available vehicles have to dock to the object, in order to move it. The optimal planning problem can be formulated as a hybrid optimal control problem. On the discrete-event level, it has to be decided how many vehicles are needed and in what sequence they will take part. The solution of the embedded continuous subproblem leads to state trajectories as well as the places and times of docking.

The continuous subproblem was solved for simple linear dynamics of the vehicles in a former thesis. Here, the extension for nonlinear dynamics has to be considered and an appropriate algorithm to be implemented. Further, combinatorial planning on the discrete-event level is investigated and implemented for the transportation scenario. Possible suitable approaches include branch-and-bound algorithms or approaches of dynamic programming.