Consensus under biased alignment

Abstract

This paper studies a consensus problem under the presence of biased alignments in two-dimensional space. The biased alignment studied in this paper may arise, for example, due to a mismatch between the control and sensing directions of the agents. After formulating the problem, we provide some sufficient conditions for consensus or for divergence depending on the biased alignments’ magnitude. Moreover, we conduct analyses on convergence characteristics in terms of locations of eigenvalues. Additionally, we study consensus conditions when the biased alignments are time-varying with errors in measured distances. Finally, several extensions of the problem on complete graphs, double-integrator dynamics, and three-dimensional space are also provided. © 2019 Elsevier Ltd