Clustering-based algorithms for multi-vehicle task assignment in a time-invariant drift field

This paper studies the multi-vehicle task assignment problem where several dispersed vehicles need to visit a set of target locations in a time-invariant drift field while trying to minimize the total travel time. Using optimal control theory, we first design a path planning algorithm to minimize the time for each vehicle to travel between two given locations in the drift field. The path planning algorithm provides the cost matrix for the target assignment, and generates routes once the target locations are assigned to a vehicle. Then, we propose several clustering strategies to assign the targets, and we use two metrics to determine the visiting sequence of the targets clustered to each vehicle. Mainly used to specify the minimum time for a vehicle to travel between any two target locations, the cost matrix is obtained using the path planning algorithm, and is in general asymmetric due to time-invariant currents of the drift field. We show that one of the clustering strategies can obtain a min-cost arborescence of the asymmetric target vehicle graph where the weight of a directed edge between two vertices is the minimum travel time from one vertex to the other respecting the orientation. Using tools from graph theory, a lower bound on the optimal solution is found, which can be used to measure the proximity of a solution from the optimal. Furthermore, by integrating the target clustering strategies with the target visiting metrics, we obtain several task assignment algorithms. Among them, two algorithms guarantee that all the target locations will be visited within a computable maximal travel time, which is at most twice of the optimal when the cost matrix is symmetric. Finally, numerical simulations show that the algorithms can quickly lead to a solution that is close to the optimal

Cooperative task assignment for multiple vehicles

Multi-vehicle systems have been increasingly exploited to accomplish difficult and complex missions, where effective and efficient coordinations of the vehicles can greatly improve the team's performance. Motivated by need from practice, we study the multi-vehicle task assignment in various challenging environments. We first investigate the task assignment for multiple vehicles in a time-invariant drift field. The objective is to employ the vehicles to visit a set of target locations in the drift field while trying to minimize the vehicles' total travel time. Using optimal control theory, a path planning algorithm is designed to generate the time-optimal path for a vehicle to travel between any two prescribed locations in a drift field. The path planning algorithm provides the cost matrix for the target assignment, and generates routes once the target locations are assigned to the vehicles. Using tools from graph theory, a lower bound on the optimal solution is found, which can be used to measure the proximity of a solution from the optimal. We propose several clustering-based task assignment algorithms in which two of them guarantee that all the target locations will be visited within a computable maximal travel time, which is at most twice of the optimal when the cost matrix is symmetric. In addition, we extend the multi-vehicle task assignment study in a time-invariant drift field with obstacles. The vehicles have different capabilities, and each kind of vehicles need to visit a certain type of target locations; each target location might have the demand to be visited more than once by different kinds of vehicles. A path planning method has been designed to enable the vehicles to move between two prescribed locations in a drift field with the minimal time while avoiding obstacles. This task assignment problem is shown to be NP-hard, and a distributed task assignment algorithm has been designed, which can achieve near-optimal solutions to the task assignment problem. Furthermore, we study the task assignment problem in which multiple dispersed heterogeneous vehicles with limited communication range need to visit a set of target locations while trying to minimize the vehicles' total travel distance. Each vehicle initially has the position information of all the targets and of those vehicles that are within its limited communication range, and each target demands a vehicle with some specified capability to visit it. We design a decentralized auction algorithm which first employs an information consensus procedure to merge the local information carried by each communication-connected vehicle subnetwork. Then, the algorithm constructs conflict-free target assignments for the communication-connected vehicles, and guarantees that the total travel distance of the vehicles is at most twice of the optimal when the communication network is initially connected. In the end we exploit the precedence-constrained task assignment problem for a truck and a micro drone to deliver packages to a set of dispersed customers subject to precedence constraints that specify which customers need to be visited before which other customers. The truck is restricted to travel in a street network and the micro drone, restricted by its loading capacity and operation range, can fly from the truck to perform the last mile package deliveries. The objective is to minimize the time to serve all the customers respecting every precedence constraint. The problem is shown to be NP-hard, and a lower bound on the optimal time to serve all the customers is constructed by using tools from graph theory. Integrating with a topological sorting technique, several heuristic task assignment algorithms are constructed to solve the task assignment problem