Mixed-integer SOCP formulation of the path planning problem for heterogeneous multi-vehicle systems

We consider the path planning problem for heterogeneous multi-vehicle systems. In such a setup an agile vehicle, which can move quickly but has limited operating range, is carried by a carrier vehicle that moves slowly but has large range. The objective is to devise an optimal path for the multi-vehicle system such that all desired points are visited as quickly as possible, while respecting all physical constraints. We show how to translate the mixed-integer nonlinear formulation of such a problem into a mixed-integer second-order cone problem that can be solved much more efficiently. The translation process employs basic concepts of propositional logic and is not conservative. Efficacy of the proposed formulation is demonstrated on a large case study.