On Consensus of Double Integrators Over Directed Graphs and with Relative Measurement Bias

Abstract

In this paper we investigate sufficient conditions for consensus of double integrators interconnected under constant directed graphs, under the condition that there exists a rooted spanning tree. We assume that only relative position as well as absolute own velocity measurements are available that is, each agent disposes of its own velocity only as well as its position relatively to that of its neighbours. In addition, it is assumed that the relative position measurements are unreliable, in the sense that they are affected by a constant bias. Under these conditions, we provide a consensus algorithm which ensures that the systems stabilize near a common equilibrium point. The analysis is based on Lyapunov direct method and a recent novel approach of analysis of networked systems that takes into account both the synchronization and the collective behavior.

Bias Estimation in Sensor Networks

“…We also apply the bias estimation algorithms to a consensus problem. Different from [40], we can prove that the system achieves exact consensus. Our algorithms do not require each node to measure the relative states of all the edges, in contrast to [11].…”

“…A similar set-up is also adopted in [39]. For second-order consensus, [40] proposes an adaptive compensator to prevent the state unboundedness caused by the biases. The proposed compensator cannot make the system achieve exact consensus.…”

“…Similar to [1], [8], [13], [20], [21], [22], [41], we assume that biased measurements can be exchanged among the neighboring nodes. Differently from [17], [40], we assume that each node has one sensor, hence the relative measurements taken by the node are affected by the same bias. The form of the system of LEs to which we reduce the problem is different from the one formulated in papers involving range or AOA measurements [11], [20]- [22].…”

Consensus of networked double integrator systems under sensor bias

“…[34] is based on the results in [14] which addresses the problem of accommodating unknown sensor bias in a direct MRAC setting for a single agent. In [35], the authors present a consensus algorithm for synchronization of double integrators over directed graphs in the presence of constant bias with unknown bounds. Here, the authors assume the existence of a bias error on each communication channel.…”

“…Similar to [34], here too convergence 'near' a common equilibrium point is guaranteed. [36] shows an extension of [34], [35] to develop a distributed consensus tracking algorithm for spacecraft in formation modeled as an Euler-Lagrange network with similar bounded performance results. For a fixed communication graph, exact constant estimation of a constant bias and consensus in single integrator agents are demonstrated in [37].…”