Consensus for Double Integrators using Binary Position Information with No Velocity Measurement

Abstract

This paper proposes a consensus protocol for multiple double integrators using binary relative position measurements under a detailed-balanced digraph. In this protocol, an agent only requires two values to measure the positive and negative relative position of its neighbors. Compared to the existing binary measurement-based protocols, the presented protocol is free from agents' velocity measurements. The non-smooth Lyapunov analysis is utilized to establish that consensus is guaranteed under the proposed protocol for any detailed-balanced digraph with any positive gains. With numerical simulations, the proposed protocol is compared with the pre-vious binary measurement-based protocol to show that the performance under the proposed protocol is least affected despite the lack of velocity measurements.