The Laplacian Artificial Potential Field (LAPF) for the Path Planning of Robotic Manipulators

This paper presents the construction of the artificial potential field based on discrete solution to the Laplace equation (Laplacian artificial potential field, LAPF), for path planning of robotic manipulators in two-dimensional and three-dimensional representations of the configuration space (C-space). In general, the characterization of the manipulator's workspace using the LAPF derives in obtaining a local minima space free when considering the combination of the manipulator's goal (position / orientation) as an attractive potential while obstacles are modeled as repulsive potentials.In addition it is shown the construction of three-dimensional configurations space, for a three-degree of freedom planar manipulator, with different arrangements stationary obstacles, of punctual type and bar type. In order to show the complexity of the space planning into the configuration space, as a result of the mapping of the obstacles within the manipulator's workspace not homogeneous to their representation in the joint's space.