A language for robot path planning in discrete environments: The TSP with Boolean satisfiability constraints

In this paper we introduce a new language in which discrete path planning problems for mobile robots can be specified and solved. Given an environment represented as a graph and a Boolean variable for each vertex to represent its inclusion/exclusion on the path, we consider the problem of finding the shortest path (or tour) in the graph subject to a Boolean satisfiability (Sat) formula defined over the vertex variables. We call this problem Sat-Tsp. We show the expressiveness of this language for specifying complex motion planning objectives in a discrete environment. We then present three solution techniques for this problem, including a novel reduction to the well known travelling salesman problem (Tsp). We present extensive simulation results which compare the performance of the three solvers on standard benchmarks from Tsp, Sat, and Generalized Tsp (Gtsp) literature.