Approximate Consensus of Multiagent Systems With Inaccurate Sensor Measurements

Abstract

One of the main challenges in robotics applications is dealing with inaccurate sensor data. Specifically, for a group of mobile robots, the measurement of the exact location of the other robots relative to a particular robot is often inaccurate due to sensor measurement uncertainty or detrimental environmental conditions. In this paper, we address the consensus problem for a group of agent robots with a connected, undirected, and time-invariant communication graph topology in the face of uncertain interagent measurement data. Using agent location uncertainty characterized by norm bounds centered at the neighboring agent's exact locations, we show that the agents reach an approximate consensus state and converge to a set centered at the centroid of the agents' initial locations. The diameter of the set is shown to be dependent on the graph Laplacian and the magnitude of the uncertainty norm bound. Furthermore, we show that if the network is all-to-all connected and the measurement uncertainty is characterized by a ball of radius r, then the diameter of the set to which the agents converge is 2r. Finally, we also formulate our problem using set-valued analysis and develop a set-valued invariance principle to obtain set-valued consensus protocols. Two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approximate consensus protocol framework.

Set-Membership Filtering-Based Leader-Follower Synchronization of Discrete-time Linear Multi-Agent Systems

“…Although the set-theoretic or set-valued concepts for synchronization have been investigated in the existing literature (see, for example, Refs. [27][28][29][30]), studies explicitly utilizing set-membership or set-valued estimation techniques for the multi-agent synchronization problem are relatively rare (see, for instance, Refs. [13,14]), despite the practical significance of this class of estimators/filters.…”

Optimal synchronization control for heterogeneous multi‐agent systems: Online adaptive learning solutions

“…Abdessameud and Tayebi [16] considered the high-order MASs described by multiple integrator dynamic under general directed graphs; Yang et al [3] investigated the distributed tracking control problem for a class of Euler-Lagrange MASs; Liuzza et al [17] investigated the problem of event-triggered control for the synchronization of networks of nonlinear dynamical agents; Chen et al [18] considered the consensus control of nonlinear MASs with time-delay states. In Sadikhov et al [19], the consensus problem for a group of agent robots with a connected, undirected, and time-invariant communication graph topology in the face of uncertain inter-agent measurement data was addressed. In Zhao et al [20], a distributed adaptive approach was developed for time-varying formation problem of linear MASs under directed topologies.…”