Joint Sensing Task Assignment and Collision-Free Trajectory Optimization for Mobile Vehicle Networks Using Mean-Field Games

With the increasing popularity of mobile vehicles, such as unmanned aerial vehicles (UAVs) and mobile robots, it is foreseen that they will play an important role in Internet-of-Things (IoT) networks due to their high mobility and rapid deployment. Specifically, mobile vehicles equipped with sensors act as IoT devices and can be dispatched to several sensing regions to perform sensing tasks. In this article, we consider mobile vehicles for sensing applications and investigate the corresponding joint task assignment and collision-free trajectory optimization problem. This problem is challenging as the number of involved vehicles can be very large, and to tackle the problem efficiently, we reformulate the original optimization problem into a mean-field-game (MFG) problem by simplifying the interaction between vehicles as a distribution over their state space, known as the mean-field term. To solve the MFG problem efficiently, we propose a G-prox primal-dual hybrid gradient (PDHG) algorithm that transforms the MFG problem into a saddle-point problem by defining a Lagrangian functional with a proximal operator. The complexity of this algorithm is shown to be linear with the total number of grid points in the proposed MFG problem. We provide a comprehensive theoretical analysis of the proposed model and algorithm. Numerical results together with the practical implementation on real mobile robots show that our proposed system model and algorithm are of significant effectiveness and efficiency.