Considering inter-task resource constraints in task allocation

This paper focuses on task allocation with single-task robots, multi-robot tasks and instantaneous assignment, which has been shown to be strongly NP-hard. Although this problem has been studied extensively, few efficient approximation algorithms have been provided due to its inherent complexity. In this paper, we first provide discussions and analyses for two natural greedy heuristics for solving this problem. Then, a new greedy heuristic is introduced, which considers inter-task resource constraints to approximate the influence between different assignments in task allocation. Instead of only looking at the utility of the assignment, our approach computes the expected loss of utility (due to the assigned robots and task) as an offset and uses the offset utility for making the greedy choice. A formal analysis is provided for the new heuristic, which reveals that the solution quality is bounded by two different factors. A new algorithm is then provided to approximate the new heuristic for performance improvement. Finally, for more complicated applications, we extend this problem to include general task dependencies and provide a result on the hardness of approximating this new formulation. Comparison results with the two natural heuristics in simulation are provided for both formulations, which show that the new approach achieves improved performance.