Coordinate-Free Distributed Localization and Circumnavigation for Nonholonomic Vehicles Without Position Information

Abstract

This article studies the localization and circumnavigation problem concerned with a cluster of nonholonomic vehicles independently of a uniform global coordinate. Particularly, the clustered vehicles collaboratively locate an unknown target and then circumnavigate it isometrically with desired distance and velocity. However, the vehicles have no access to any position information, including their own absolute positions and others’ relative positions. Instead, they are capable of measuring relative bearings only with respect to their neighbors within their local coordinates. Different local coordinates are not necessarily aligned. Moreover, only some of the vehicles can measure relative bearings with respect to the target. For the solution to the concerned localization and circumnavigation problem, a coordinate-free distributed algorithm composed by two parts is proposed. To be specific, the first distributed localization part guarantees that the vehicles accurately estimate the relative positions with respect to the target and neighbors given a persistently exciting condition. And the second distributed circumnavigation part further guarantees that the vehicles move around the target estimation isometrically with the desired distance and velocity. Also, the necessary persistently exciting condition is shown to be met. Finally, simulation and experiment are both given to confirm the effectiveness of the proposed distributed algorithm.