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Mathematical Problems in Engineering
Volume 2015, Article ID 105357, 11 pages
Research Article

Finding the Quickest Straight-Line Trajectory for a Three-Wheeled Omnidirectional Robot under Input Voltage Constraints

11st R&D Institute-3, Agency for Defense Development, 111 Sunam-dong, Yuseong-gu, Daejeon 305-600, Republic of Korea
2Department of Computer Science and Engineering, Kwangwoon University, 20 Kwangwoon-ro, Nowon-gu, Seoul 139-701, Republic of Korea
3Department of Computer Engineering, College of Information Technology, Gachon University, 1342 Seongnamdaero, Sujeong-gu, Seongnam-si, Gyeonggi-do 461-701, Republic of Korea

Received 27 October 2014; Revised 31 December 2014; Accepted 8 January 2015

Academic Editor: Javier Moreno-Valenzuela

Copyright © 2015 Ki Bum Kim 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.


We provide an analytical solution to the problem of generating the quickest straight-line trajectory for a three-wheeled omnidirectional mobile robot, under the practical constraint of limited voltage. Applying the maximum principle to the geometric properties of the input constraints, we find that an optimal input vector of motor voltages has at least one extreme value when the orientation of the robot is fixed and two extreme values when rotation is allowed. We can find an explicit representation of the optimal vector for a motion under fixed orientation. We derive several properties of quickest straight-line trajectories and verify them through simulation. We show that the quickest trajectory when rotation is allowed is always faster than the quickest with fixed orientation.