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Computational analysis of the Cauchy problem associated to the kinematic model of a mobile robot

Daniela Coman1 and Adela Ionescu2*

Author Affiliations

1 Department of Engineering and Management of Technological Systems, Faculty of Mechanics, University of Craiova, Craiova, Romania

2 Department of Applied Mathematics, University of Craiova, Craiova, Romania

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Boundary Value Problems 2013, 2013:138  doi:10.1186/1687-2770-2013-138

Published: 24 May 2013

Abstract

Recently, the specific problems arising to mobile robots are the following: determining the position and orientation of the robot on the field, planning an optimal path of motion and stationary or moving objects avoidance.

This paper realizes a computational analysis of the Cauchy problem associated to a mobile robot kinematics. The ‘phase portrait’ graphical tool of the mathematical soft MAPLE11 points out the influence of the initial conditions: the initial velocities of the driving (left and right) wheels of the robot on the robot trajectory. Considering a pair of two simulation cases for the initial conditions brings a good reliability of the analysis.

MSC: 68T40, 70B15, 70B10, 37M05.

Keywords:
mobile robot; differential drive; kinematic model; phase-portrait