Directional fields algebraic non-linear solution equations for mobile robot planning

In this study, a novel approach to robot navigation/planning by using half-cell electrochemical potentials is presented. The half-cell electrode’s potential is modelled by the Nernst equation to yield automatic search/detection of pipeline flaws by using the direct current voltage gradient (DCVG) te...

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Bibliographic Details
Published in:Applied mathematical modelling 2014-11, Vol.38 (21-22), p.5298-5314
Main Authors: Martínez-García, Edgar A., Torres Córdoba, Rafael, Martínez-Villafañe, Alberto, Floriano Gabaldón, Luis
Format: Article
Language:English
Subjects:
Algebra
Defects
Directional fields
Mathematical analysis
Mathematical models
Modelling
Non-holonomy robotics
Nonlinear equations
Nonlinearity
Planning
Robot control
Robots
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Summary:In this study, a novel approach to robot navigation/planning by using half-cell electrochemical potentials is presented. The half-cell electrode’s potential is modelled by the Nernst equation to yield automatic search/detection of pipeline flaws by using the direct current voltage gradient (DCVG) technique. We introduce a theory of spherical volumetric electric density in the soil to sustain our postulates for navigational potential fields. The Nernst potential is correlated with the distance to a pipe’s flaw by proposing a fitted theoretical-empirical nonlinear regression model. From this, volumetric derivatives are solved as gradient-based fields to control wheeled robot’s motion. A nonlinear system for trajectory planning is proposed, and analytically solved by an algebraic solution. This solution directly adjust robot’s speed kinematic values to lead it toward the flaw. The inverse/forward kinematic constraints are non-holonomic, and are recursively integrated into the general potential equation. Analytical modelling is reported, and a set of numerical simulations are presented to prove the feasibility of the proposed formulations.
ISSN:0307-904X
DOI:10.1016/j.apm.2014.04.013