Article (Scientific journals)
Consensus and Formation Control on SE(3) for Switching Topologies
Thunberg, Johan; Goncalves, Jorge; Hu, Xiaoming
2016In Automatica, 66, p. 14
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Keywords :
Attitude synchronization; Formation control; Networked robotics
Abstract :
[en] This paper addresses the consensus problem and the formation problem on SE(3) in multi-agent systems with directed and switching interconnection topologies. Several control laws are introduced for the consensus problem. By a simple transformation, it is shown that the proposed control laws can be used for the formation problem. The design is first conducted on the kinematic level, where the velocities are the control laws. Then, for rigid bodies in space, the design is conducted on the dynamic level, where the torques and the forces are the control laws. On the kinematic level, first two control laws are introduced that explicitly use Euclidean transformations, then separate control laws are defined for the rotations and the translations. In the special case of purely rotational motion, the consensus problem is referred to as consensus on SO(3) or attitude synchronization. In this problem, for a broad class of local representations or parameterizations of SO(3), including the Axis–Angle Representation, the Rodrigues Parameters and the Modified Rodrigues Parameters, two types of control laws are presented that look structurally the same for any choice of local representation. For these two control laws we provide conditions on the initial rotations and the connectivity of the graph such that the system reaches consensus on SO(3). Among the contributions of this paper, there are conditions for when exponential rate of convergence occurs. A theorem is provided showing that for any choice of local representation for the rotations, there is a change of coordinates such that the transformed system has a well known structure.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Thunberg, Johan ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Goncalves, Jorge ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Hu, Xiaoming;  KTH Royal Institute of Technology > Department of mathematics
External co-authors :
yes
Language :
English
Title :
Consensus and Formation Control on SE(3) for Switching Topologies
Publication date :
2016
Journal title :
Automatica
ISSN :
0005-1098
Publisher :
Pergamon Press - An Imprint of Elsevier Science, Oxford, United Kingdom
Volume :
66
Pages :
14
Peer reviewed :
Peer Reviewed verified by ORBi
FnR Project :
FNR8864515 - Set Convergence In Nonlinear Multi-agent Systems, 2014 (01/02/2015-31/01/2017) - Johan Thunberg
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