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Finite‐time formation tracking control for multiple vehicles: A motion planning approach
Author(s) -
Liu Yongfang,
Zhao Yu,
Chen Guanrong
Publication year - 2015
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.3496
Subject(s) - tracking (education) , control theory (sociology) , euclidean group , trajectory , pontryagin's minimum principle , task (project management) , control (management) , function (biology) , maximum principle , computer science , euclidean geometry , optimal control , motion (physics) , track (disk drive) , mathematics , mathematical optimization , engineering , artificial intelligence , physics , pedagogy , systems engineering , affine transformation , affine space , biology , operating system , psychology , geometry , evolutionary biology , astronomy , pure mathematics
Summary This paper addresses the finite‐time formation tracking problem for multiple vehicles with dynamics model on SE(3) (the specific Euclidean group of rigid body motions), under the condition that the tracking time is preassigned according to the task requirements. By using Pontryagin's maximum principle on Lie groups, a class of finite‐time optimal tracking control laws are designed for vehicles to track a desired trajectory within a given finite time. Meanwhile, the corresponding cost function is minimized. Furthermore, a tracking‐time lower bound is derived for multi‐vehicle systems with control constraints. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control laws. Copyright © 2015 John Wiley & Sons, Ltd.