Optimal vehicle routing with interception of targets´ neighbourhoods

We consider the task of devising a planar route of minimal distance which starts from a given starting point, passes through neighbourhoods of pre-defined target points, e.g. by priorities, and ends at a prescribed finishing location. Two types of routes are considered. A piecewise linear route is of minimal possible length, but introduces sharp turns. To mitigate this issue, we also consider a smooth polynomial path. In addition, we also show how to construct a path that is smooth and has a bounded curvature. Such an extension allows to devise optimal routing for vehicles that have limited turning capabilities. To allow for greater design flexibility, we also consider piecewise polynomial routes with enforced continuity in first and second derivatives.