A randomized greedy algorithm for piecewise linear motion planning

Simplicial complexity (SC) is a discretized model for Farber's topological complexity (TC) of an autonomous system whose space of states is a polyhedron $K$. We describe a randomized algorithm that, given $K$, finds an explicit system of SC motion planners. An implementation of this algorithm revels that, unlike other discrete approached in the literature to Farber's TC, the SC approach performs satisfactorily well without having to introduce costly subdivisions of $K$.