Distributed Algorithms for Multirobot Task Assignment With Task Deadline Constraints

Abstract

We present distributed algorithms for multirobot task assignment where the tasks have to be completed within given deadlines. Each robot has a limited battery life and thus there is an upper limit on the amount of time that it has to perform tasks. Performing each task requires certain amount of time (called the task duration) and each robot can have different payoffs for the tasks. Our problem is to assign the tasks to the robots such that the total payoff is maximized while respecting the task deadline constraints and the robot's battery life constraints. Our problem is NP-hard since a special case of our problem is the classical generalized assignment problem (which is NP-hard). There are no known algorithms (distributed or centralized) for this problem with provably good guarantees of performance. We present a distributed algorithm for solving this problem and prove that our algorithm has an approximation ratio of 2. For the special case of constant task duration we present a distributed algorithm that is provably almost optimal. Our distributed algorithms are polynomial in the number of robots and the number of tasks. We also present simulation results to depict the performance of our algorithms. Note to Practitioners-In this paper, we present provably good multirobot task assignment algorithms, while considering practical constraints like task deadlines and limited battery life of robots. Such constraints are relevant in many applications including parts movement by robots in manufacturing, delivery of goods by unmanned vehicles, and search and rescue operations. Our solution is applicable to a group of heterogeneous robots with different suitability (i.e., payoffs) for different tasks. Our distributed approach is independent of the underlying robot communication network topology, and thus can be applied to a wide range of robot network deployments. Finally, our approach is easy to implement, has low communication requirements, and it is scalable, since its - unning time is linear in the number of robots and tasks.