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

机译：移动机器人规划的方向场代数非线性解方程

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摘要

In this study, a novel approach to robot navigation/planning by using half-cell electro-chemical 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.
机译：在这项研究中，提出了一种通过使用半电池电化学势来进行机器人导航/规划的新颖方法。半能电池电极的电势由能斯特方程式建模，可以使用直流电压梯度（DCVG）技术自动搜索/检测管道缺陷。我们介绍了土壤中球形体积电密度的理论，以维持航行势场的假设。通过提出拟合的理论-经验非线性回归模型，能斯特势与到管道缺陷的距离相关。由此，将体积导数作为基于梯度的场进行求解，以控制轮式机器人的运动。提出了一种用于轨迹规划的非线性系统，并通过代数解决方案进行了解析求解。该解决方案直接调整机器人的速度运动学值，使其趋向缺陷。反向/正向运动学约束是非完整的，并且被递归集成到一般势方程中。报告了分析模型，并提出了一组数值模拟，以证明所提出的配方的可行性。

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