Optimal Control of an Underwater Sensor Network for Cooperative Target Tracking

Optimal control (OC) is a general and effective approach for trajectory optimization in dynamical systems. So far, however, it has not been applied to mobile sensor networks due to the lack of suitable objective functions and system models. In this paper, an integral objective function representing the quality of service of a sensor network performing cooperative track detection over time is derived using a geometric transversals approach. A set of differential equations modeling the sensor network's dynamics is obtained by considering three dependent subsystems, i.e., underwater vehicles, onboard sensors, and oceanographic fields. Each sensor-equipped vehicle is modeled as a bounded subset of a Euclidian space, representing the sensor's field of view (FOV), which moves according to underwater vehicle dynamics. By this approach, the problem of generating optimal sensors' trajectories is formulated as an OC problem in computational geometry. The numerical results show that OC significantly improves the network's quality of service compared to area-coverage and path-planning methods. Also, it can be used to incorporate sensing and energy constraints on the sensors' state and control vectors, and to generate fronts of Pareto optimal trajectories.