Autonomous Navigation in Static Indoor Environment via Rotated Laplacian Operator

One of the main aim in autonomous robot navigation is to solve path planning problem. This problem refers to the ability of an autonomous robot to move from arbitrary start location to a specified goal location without colliding with any obstacles while traveling. In robotics literature, most path planning approaches based on harmonic potentials relies on the use of the standard 5-point Laplacian operator. In this paper, the performance of a rotated 5-point Laplacian operator for computing the harmonic potentials is investigated. By using this rotated operator, a system of algebraic rotated approximation equations is constructed. This algebraic rotated linear system is computed using Half-Sweep Accelerated Over-Relaxation (HSAOR) iterative method. The performance of the HSAOR algorithm that employed the proposed rotated Laplacian operator is compared and analyzed against the existing algorithms in terms of number of iterations and execution time. The results show that the HSAOR method performed better than the existing methods.