Consensus of networked double integrator systems under sensor bias

TL;DR

This paper introduces an adaptive distributed control law enabling networked double integrator systems to achieve consensus despite sensor biases, by estimating biases and ensuring exponential convergence.

Contribution

It presents a novel adaptive control strategy that jointly estimates sensor biases and achieves consensus, extending previous methods to biased measurement scenarios.

Findings

Achieves exponential position consensus despite sensor bias

Develops conditions linking graph structure and bias estimation

Validates approach through simulation studies

Abstract

A novel distributed control law for consensus of networked double integrator systems with biased measurements is developed in this article. The agents measure relative positions over a time-varying, undirected graph with an unknown and constant sensor bias corrupting the measurements. An adaptive control law is derived using Lyapunov methods to estimate the individual sensor biases accurately. The proposed algorithm ensures that position consensus is achieved exponentially in addition to bias estimation. The results leverage recent advances in collective initial excitation based results in adaptive estimation. Conditions connecting bipartite graphs and collective initial excitation are also developed. The algorithms are illustrated via simulation studies on a network of double integrators with local communication and biased measurements.