Observer-Based Control of Second-Order Multi-vehicle Systems in Bearing-Persistently Exciting Formations

TL;DR

This paper develops an observer-based control method for second-order multi-vehicle formations using only bearing measurements, ensuring stability and localization without requiring vehicles' position data.

Contribution

It introduces new algorithms for bearing-based localization and state estimation, and analyzes stability conditions for formation control with limited measurement data.

Findings

Proposed algorithms achieve accurate localization and control in simulations.

Stability conditions ensure exponential convergence of the formation tracking.

The approach works with minimal measurement data, only bearings and accelerations.

Abstract

This paper proposes an observer-based formation tracking control approach for multi-vehicle systems with second-order motion dynamics, assuming that vehicles' relative or global position and velocity measurements are unavailable. It is assumed that all vehicles are equipped with sensors capable of sensing the bearings relative to neighboring vehicles and only one leader vehicle has access to its global position. Each vehicle estimates its absolute position and velocity using relative bearing measurements and the estimates of neighboring vehicles received over a communication network. A distributed observer-based controller is designed, relying only on bearing and acceleration measurements. This work further explores the concept of the \textit{Bearing Persistently Exciting} (BPE) formation by proposing new algorithms for bearing-based localization and state estimation of second-order systems in centralized and decentralized manners. It also examines conditions on the desired formation to guarantee the exponential stability of distributed observer-based formation tracking controllers. In support of our theoretical results, some simulation results are presented to illustrate the performance of the proposed observers as well as the observer-based tracking controllers.