Distributed multi-vehicle task assignment in a time-invariant drift field with obstacles

What is it about?

This paper investigates the task assignment problem where a fleet of dispersed vehicles needs to visit multiple target locations in a time-invariant drift field with obstacles while trying to minimize the vehicles’ total travel time. The vehicles have different capabilities, and each kind of vehicles can visit a certain type of the target locations; each target location might require to be visited more than once by different kinds of vehicles. We prove that the task assignment problem is in fact NP-hard. A path planning algorithm is first designed to minimize the time for a vehicle to travel between two given locations through the drift field while avoiding any obstacle. The path planning algorithm provides the travel cost matrix for the target assignment, and generates routes once the target locations are assigned to the vehicles. Then, we design a distributed algorithm to assign the target locations to the vehicles using only local communication. The algorithm guarantees that all the visiting demands of every target will be satisfied within a total travel time that is at worst twice of the optimal when the travel cost matrix is symmetric. Numerical simulations show that the algorithm can lead to solutions close to the optimal.

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