Chance Constrained Simultaneous Path Planning and Task Assignment for Multiple Robots with Stochastic Path Costs

We present a novel algorithm for simultaneous task assignment and path planning on a graph (or roadmap) with stochastic edge costs. In this problem, the initially unassigned robots and tasks are located at known positions in a roadmap. We want to assign a unique task to each robot and compute a path for the robot to go to its assigned task location. Given the mean and variance of travel cost of each edge, our goal is to develop algorithms that, with high probability, the total path cost of the robot team is below a minimum value in any realization of the stochastic travel costs. We formulate the problem as a chance-constrained simultaneous task assignment and path planning problem (CC-STAP). We prove that the optimal solution of CC-STAP can be obtained by solving a sequence of deterministic simultaneous task assignment and path planning problems in which the travel cost is a linear combination of mean and variance of the edge cost. We show that the deterministic problem can be solved in two steps. In the first step, robots compute the shortest paths to the task locations and in the second step, the robots solve a linear assignment problem with the costs obtained in the first step. We also propose a distributed algorithm that solves CC-STAP near-optimally. We present simulation results on randomly generated networks and data to demonstrate that our algorithm is scalable with the number of robots (or tasks) and the size of the network.