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

This paper presents the application of a two-stage HalfSweep 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.