Computationally Tractable Formulations for Optimal Path Planning with Interception of Targets’ Neighborhoods

Abstract

Devising the planar routes of minimal length that are required to pass through predefined neighborhoods of target points plays an important role in reducing the mission’s operating cost. Two versions of the problem are considered. The first one assumes that the ordering of the targets is fixed a priori. In such a case, the optimal route is devised by solving a convex optimization problem formulated either as a second-order cone program or as a sum-of-squares optimization problem. Additional route properties, such as continuity and minimal curvature, are considered as well. The second version allows the ordering of the targets to be optimized to further reduce the route length. We show that such a problem can be solved by introducing additional binary variables, which allows the route to be designed using off-the-shelf mixed-integer solvers. A case study that shows that the proposed strategy is computationally tractable is presented.