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Trajectory tracking of nonholonomic mobile robots by geometric control on special Euclidean group
Author(s) -
He Xiaodong,
Geng Zhiyong
Publication year - 2021
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.5561
Subject(s) - euclidean group , control theory (sociology) , nonholonomic system , mobile robot , trajectory , group (periodic table) , nonlinear system , computer science , mathematics , controller (irrigation) , euclidean space , robot , control (management) , artificial intelligence , pure mathematics , physics , affine space , chemistry , organic chemistry , quantum mechanics , astronomy , affine transformation , agronomy , biology
This article studies the trajectory tracking of nonholonomic mobile robots by using geometric control methods, with extension to consensus tracking and formation tracking. Different from the system model given in the Euclidean space, we establish the dynamics of mobile robots on the tangent bundle of the Lie group, which is a global and unique description independent of local coordinates. Firstly, the tracking control of one leader with one follower is considered, which is converted to the stabilization of two relative subsystems by designing an adjoint system. Then, the controller is extended to consensus tracking of multiple robots connected by a directed acyclic graph, where the convex combination on nonlinear manifolds is introduced to construct a virtual leader for each follower. Next, the relation between consensus control and formation control is established, and a new transformed system is constructed so as to derive the formation tracking controller from the consensus result. Finally, simulation examples are presented to verify the effectiveness of the proposed controllers.