Finding a Collision-free Trajectory Using Electric Field Analysis and L1-norm

Abstract

This paper addresses the problem of finding a collision-free trajectory between two points with known positions using the electric field concept. Analogous to an electric dipole, two strong electric point charges with opposite signs (positive and negative) are positioned in the navigation space at the starting and target points, respectively. Additionally, static obstacles are represented as slightly negative point charges. In this scenario, a hypothetical positive charge is considered a mobile particle that is released from the starting position with a specific angle in the vector field map sketched by the field lines created by the electric dipole. The trajectory produced by this hypothetical charge constitutes a path for avoiding obstacles from the origin to the destination points. To ensure that the computed trajectory remains inside a specified area, the navigation space is bounded by a rectangular border generated by a vector field function. Furthermore, to reduce the computational cost of the field map calculation (running time and memory consumption), the L1-norm is employed to describe distances instead of the traditional L2-norm (Euclidean norm). Numerical simulations demonstrate the effectiveness of this approach, as well as the reduction in computational cost by using the L1-norm.