Joint Task Assignment and Trajectory Optimization for a Mobile Robot Swarm by Mean-Field Game

摘要

In recent years, there has been a growing interest in utilizing mobile robot swarm to execute several tasks at the same time. However, how to assign tasks to the swarm and optimize the trajectory of the robots scientifically to minimize energy consumption is still a big challenge. In this paper, we consider a mobile robot swarm system where a large number of robots are deployed by a centralized controller to execute a series of tasks, such as target detection tasks, cooperatively. The controller controls the velocity strategy of each robot, and makes corresponding task assignment decisions to minimize the overall cost of the robot swarm. Since the number of involving robots is large, it will be extremely difficult to consider the interaction between them. In this regard, we adopt the concept of mean-field term to approximate the behaviors and states of the robots, and formulate the joint task assignment and trajectory optimization problem as a mean-field game. To solve the problem efficiently, a primal-dual hybrid gradient algorithm is proposed to find the optimal trajectory and corresponding task assignment decisions for each robot. The numerical simulation results show the effectiveness of the proposed algorithm.