  The main contribution of this paper is a novel method for planning globally
optimal trajectories for dynamical systems subject to polygonal constraints.
The proposed method is a hybrid trajectory planning approach, which combines
graph search, i.e. a discrete roadmap method, with convex optimization, i.e. a
complete path method. Contrary to past approaches, which have focused on using
simple obstacle approximations, or sub-optimal spatial discretizations, our
approach is able to use the exact geometry of polygonal constraints in order to
plan optimal trajectories. The performance and flexibility of the proposed
method is evaluated via simulations by planning distance-optimal trajectories
for a Dubins car model, as well as time-, distance- and energy-optimal
trajectories for a marine vehicle.
