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Mathematical Problems in Engineering
Volume 2016, Article ID 8606570, 13 pages
Research Article

Finite Time Controller for Point Stabilization of a Spherical Underwater Roving Robot

Institute of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received 21 April 2016; Revised 25 July 2016; Accepted 8 August 2016

Academic Editor: Ricardo Aguilar-López

Copyright © 2016 Zhimin Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The finite time controller is proposed to solve the point stabilization problem for a novel underwater spherical roving robot (BYSQ-3) in two-dimensional space. The finite time design scheme is a new method; the main advantage of this control scheme is that it can steer the robot to the origin in fast converging times without excessive control effort. Firstly, the physical prototype of BYSQ-3 is introduced and the equations describing the kinematics and dynamics of BYSQ-3 are established. Secondly, the finite time controller is constructed based on the backstepping method; the explicit form of the finite time controller is more concise compared with the other finite time controllers; there is no virtual input in the design process and the stability analysis is simple; the designed controller is easy for engineering implementation. Thirdly, the hydrodynamic characteristics is analyzed by CFD simulation; the simulation and experiment results are presented to validate the shorter convergence time and better stability character of the controller.