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Finite-time formation tracking control for multiple vehicles A motion planning approach RNC 2016.pdf

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Finite-time formation tracking control for multiple vehicles A motion planning approach RNC 2016

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2016; 26:3130–3149 Published online 17 December 2015 in Wiley Online Library (). DOI: 10.1002/rnc.3496 Finite-time formation tracking control for multiple vehicles: A motion planning approach Yongfang Liu1,*,? , Yu Zhao1 and Guanrong Chen2 1School of Automation, Northwestern Polytechnical University, Xian 710072, China 2Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong 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. Received 2 July 2015; Revised 2 November 2015; Accepted 12 November 2015 KEY WORDS: finite-time; optimal control; formation tracking; Lie group 1. INTRODUCTION Over the past few years, control and coordination of multiple autonomous vehicles have been of great interest to various scientific and engineering communities because of broad applications in such fields as robot manipulators, motion control of underwater maneuvers, aerospace autonomous vehicles, and so forth [1, 2]. One of the distinct features of these systems is that their configura- tion manifolds are nonlinear. Considering only rotation of such a system, it typically evolves on the nonlinear manifold SO(3), which is the matrix Lie group of 3 3 orthogonal mat