Numerical simulations of agent navigation via Half-Sweep Modified Two-Parameter Over-Relaxation (HSMTOR)

Abstract

The research on the efficiency of route navigation has been continuously developing. Especially, the capability of the generated route to provide a collision-free route for an agent to move in a particular environment. Thus, this study attempts to solve the route navigational problem iteratively via a numerical method. A new method called Half-Sweep Modified Two-Parameter Over-Relaxation (HSMTOR) is used to solve the navigational problems. For numerical simulation purposes, HSMTOR is used to obtain Laplace’s equation solutions called harmonic functions. A gradient descent search algorithm then utilizes the harmonic functions to provide a smooth and collision-free route for an agent to commute inside the environment. In addition, the formulation of the HSMTOR iterative method is presented. Several numerical experiments and simulations are conducted in order to verify the efficiency of the proposed method. The result shows that the proposed method performed better than the existing methods such as full-, half-sweep for Modified Successive Over-Relaxation, Modified Accelerated Over-Relaxation and Modified Two-Parameter Over-Relaxation respectively (FSMSOR, HSMSOR, FSMAOR, HSMAOR and FSMTOR).

Half-sweep Modified SOR Approximation of A Two-dimensional Nonlinear Parabolic Partial Differential Equation

“…Then, the results by [14] showed HSMSOR method has better efficiency than successive over-relaxation methods in solving linear systems after the cubic spline scheme was implemented. Due to the potential of the HSMSOR method, [15,16] applied the method to simulate indoor mobile robots' path planning and agent navigations, respectively. Since nonlinear problems are more realistic to be solved, [17] initiated the investigation of solving one-dimensional NPPDE using their HSMSOR method.…”