Harmonic Path Planning using Two-Stage Half- Sweep Arithmetic Mean Method

Abstract

This paper presents the application of a two-stage Half-Sweep Arithmetic Mean (HSAM) iterative method for computing the solution of Laplace's equation (also known as harmonic functions) in two-dimensional space to solve the path planning problem in indoor environment. Several path planning simulations in a known indoor environment were conducted to examine the effectiveness of the proposed method. It is shown that the designed path planning algorithm is capable of generating smooth paths from various start and goal positions. Also, numerical results show that the proposed HSAM method converges much faster than the existing iterative methods, thus it drastically improves the overall performance of the path planning algorithm.

Autonomous path planning through application of rotated two-parameter overrelaxation 9-point Laplacian iteration technique

“…Nonetheless, the integration of APF with suitable methods such as the study in [14] could provide benefits for autonomous path planning improvement. Due to its attractive properties, harmonic functions are a popular choice in solving path planning problems [15]- [17]. Through harmonic functions, which are also solutions to Laplace's equation, no local minimum is generated during path planning computations [9], [18].…”