Consensus of Multiagent System in the Sense of Curvature and Torsion

Abstract

In this paper, the consensus problem is investigated for a distributed multiagent system (MAS), where the consensus is characterized by curvature function and torsion function. According to the Frenet-Serret formulas, a distributed consensus protocol is designed for the tangent, normal, and binormal unit vectors of trajectory of each agent, and then it gets a closed-loop system. Based on the Lyapunov function, several sufficient conditions for consensus are derived for the closed-loop system. Also the consensus problem of multiagent system on a surface is studied. Finally, the numerical examples show the reliability of the proposed methods.

Curvature- and Torsion-Based Consensus for the Markovian Switching Multiagent System with Communication of Noise Disturbance and Time Delay

“…where ] is a real number, and ] < 1, 2q ι σ ι ≤ 1, then system (31) is asymptotically stable, where λ 2 is the second largest eigenvalue of L, A − 2 � diag ω 1 , ω 2 , . .…”

“…If all agents keep the same curvature function and torsion function, then they can move with the same track, and they can keep a certain distance among them. Recently, the consensus problem of MAS in the sense of curvature and torsion with fixed topology was studied in literature [31]. However, the results may not suitable to the switching system with stochastic disturbance.…”

“…where ] is a real number, and ] < 1, ]e aς 1 � 1, then system ( 31) is asymptotically stable. erefore, system (31) is the BCT consensus.…”