Cooperative navigation using constrained convex generators

Abstract

In this article, we suggest a technique of set-based cooperative navigation for a fleet of vehicles under communication constraints. In the suggested approach, only the distances and bearings to other vehicles or known locations can be measured. Each vehicle in the fleet must determine its location and the positions of the other vehicles based on the measurements as well as information shared among the vehicles. Since the measurement set may be nonconvex, it must be approximated by a convex set. To address this issue, we employ constrained convex generators, which is a generalization of the definition for constrained zonotopes that allows ${\ell }_2$ unit norm balls and convex cones. To keep the amount of exchanged information low the vehicles transmit an ellipse containing the state estimate to the other vehicles. The obtained estimates are worst-case bounds for the true position, which is important in certain applications such as collision avoidance. The computed sets are then applied to vehicle control algorithms, taking into account the positions of all the agents. Through numerical simulations, we illustrate the application of this method to the problem of cooperative navigation of autonomous underwater vehicles and the problem of fire detection with multiple UAVs.