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Robust formation control of multiagent systems on the Lie group S E (3)
Author(s) -
Ghasemi Kobra,
Ghaisari Jafar,
Abdollahi Farzaneh
Publication year - 2019
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4806
Subject(s) - control theory (sociology) , multi agent system , singularity , kinematics , computer science , sliding mode control , adaptive control , estimator , mathematics , control (management) , artificial intelligence , mathematical analysis , statistics , physics , classical mechanics , nonlinear system , quantum mechanics
Summary This paper addresses the robust formation control problem of multiple rigid bodies whose kinematics and dynamics evolve on the Lie group S E (3). First, it is assumed that all followers have access to the state information of a virtual leader. Then, a novel adaptive super‐twisting sliding mode control with an intrinsic proportional‐integral‐derivative sliding surface is proposed for the formation control problem of multiagent system using a virtual structure (VS) approach. The advantages of this control scheme are twofold: elimination of the chattering phenomenon without affecting the control performance and no requirement of prior knowledge about the upper bound of uncertainty/disturbance due to adaptive‐tuning law. Since the VS method is suffering from the disadvantages of centralized control, in the second step, considering a network as an undirected connected graph, we assume that only a few agents have access to the state information of the leader. Afterward, using the gradient of modified error function, a distributed adaptive velocity‐free consensus‐based formation control law is proposed where reduced‐order observers are introduced to remove the requirements of velocity measurements. Furthermore, to relax the requirement that all agents have access to the states of the leader, a distributed finite‐time super‐twisting sliding mode estimator is proposed to obtain an accurate estimation of the leader's states in a finite time for each agent. In both steps, the proposed control schemes are directly developed on the Lie group S E (3) to avoid singularity and ambiguities associated with the attitude representations. Numerical simulation results illustrated the effectiveness of the proposed control schemes.