Collocation Methods for Multi-Vehicle Trajectory Optimization

Direct collocation offers an efficient way of transcribing optimal control problems to form nonlinear optimizations. Collocation is particularly attractive for variable time problems as the finishing time can be made a decision variable. However, this causes problems in coupled multi-vehicle problems, for example, where different vehicles may have different finishing times. This paper proposes a way of capturing coupling constraints - in particular, collision avoidance - between vehicles without requiring a common time of arrival. The approach exploits a recently-developed dualization approach for avoidance constraints, extended to act time as well as spatial dimensions.