Phase Transitions in the Multi-Vehicle Task Assignment Problem
Matthew G. Earl, Raffaello D’Andrea · 2005
We have developed real-time methods to synthesize cooperative strategies for the multi-vehicle task assignment problem in an adversarial environment. By introducing a set of tasks to be completed by the team of vehicles and a trajectory generation primitive for each vehicle, we formulate the multi-vehicle control problem as a task assignment problem. The continuous component of the problem is captured by the trajectory primitive, and the combinatorial component is captured by task assignment. We have developed an efficient branch and bound solver for the task assignment component of the problem. In this paper, we analyze the computational complexity of our solver with variations in parameters of the problem. We found a phase transition in the ratio of the maximum velocity of opposing vehicles, and we found a phase transition in the ratio of the number of vehicles per team. The results show that the task assignment problem is difficult to solve when the capabilities of the two teams are comparable and easy to solve when one team is more capable than the other.