Path Planning for Mobile Robot using 4EGSOR via Nine-Point Laplacian (4EGSOR9L) Iterative Method

Saudi, Azali; Sulaiman, Jumat

doi:10.5120/8509-2568

Cited by 13 publications

(12 citation statements)

References 19 publications

(17 reference statements)

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“…By this way, the computational complexity can be reduced by solving several small groups of points instead of a large linear system per iteration. The EG method has been used extensively together with some efficient iterative methods such as SOR, MSOR and AOR [13][14][15]. Before the EG method is applied, equation 17can be transformed into a linear system by using the Newton method as follows:…”

Section: Derivation Of the Four-point Negmsor Iterative Methodsmentioning

confidence: 99%

An unconditionally stable implicit difference scheme for 2D porous medium equations using four-point NEGMSOR iterative method

Lung

Sulaiman

2018

ITM Web Conf.

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In this paper, a numerical method has been proposed for solving several two-dimensional porous medium equations (2D PME). The method combines Newton and Explicit Group MSOR (EGMSOR) iterative method namely four-point NEGMSOR. Throughout this paper, an initialboundary value problem of 2D PME is discretized by using the implicit finite difference scheme in order to form a nonlinear approximation equation. By taking a fixed number of grid points in a solution domain, the formulated nonlinear approximation equation produces a large nonlinear system which is solved using the Newton iterative method. The solution vector of the sparse linearized system is then computed iteratively by the application of the four-point EGMSOR method. For the numerical experiments, three examples of 2D PME are used to illustrate the efficiency of the NEGMSOR. The numerical result reveals that the NEGMSOR has a better efficiency in terms of number of iterations, computation time and maximum absolute error compared to the tested NGS, NEG and NEGSOR iterative methods. The stability analysis of the implicit finite difference scheme used on 2D PME is also provided.

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Section: Derivation Of the Four-point Negmsor Iterative Methodsmentioning

confidence: 99%

An unconditionally stable implicit difference scheme for 2D porous medium equations using four-point NEGMSOR iterative method

Lung

Sulaiman

2018

ITM Web Conf.

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“…Harmonic functions describe flow dynamics by means of the Laplace equation, where the potential field is free of local minima and produces a set of streamlines ( [7,8,[11][12][13]). These streamlines are time-independent and describe the movement of a massless fluid element traveling from a start to a target position, following the velocity field derived from the potential field gradient as in (11).…”

Section: Navigation Examplementioning

confidence: 99%

“…The only profit of this methodology is when the environment remains static, which is not the standard situation. In spite of this, some techniques have sped up this computation ( [12,13]), but the computational burden is still high for RT path planning, with 646s for an environment with 512 × 512 nodes using the EGSOR algorithm in [13].…”

Section: Introductionmentioning

confidence: 99%

A Path Planning Algorithm for a Dynamic Environment Based on Proper Generalized Decomposition

et al. 2020

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A necessity in the design of a path planning algorithm is to account for the environment. If the movement of the mobile robot is through a dynamic environment, the algorithm needs to include the main constraint: real-time collision avoidance. This kind of problem has been studied by different researchers suggesting different techniques to solve the problem of how to design a trajectory of a mobile robot avoiding collisions with dynamic obstacles. One of these algorithms is the artificial potential field (APF), proposed by O. Khatib in 1986, where a set of an artificial potential field is generated to attract the mobile robot to the goal and to repel the obstacles. This is one of the best options to obtain the trajectory of a mobile robot in real-time (RT). However, the main disadvantage is the presence of deadlocks. The mobile robot can be trapped in one of the local minima. In 1988, J.F. Canny suggested an alternative solution using harmonic functions satisfying the Laplace partial differential equation. When this article appeared, it was nearly impossible to apply this algorithm to RT applications. Years later a novel technique called proper generalized decomposition (PGD) appeared to solve partial differential equations, including parameters, the main appeal being that the solution is obtained once in life, including all the possible parameters. Our previous work, published in 2018, was the first approach to study the possibility of applying the PGD to designing a path planning alternative to the algorithms that nowadays exist. The target of this work is to improve our first approach while including dynamic obstacles as extra parameters.

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“…The mobile robot is represented by a point in the Cspace. This setup will create a heat conduction process in which there will be temperature distributions, or in the robotics term, potential values [14]. The outer and inner wall boundaries, together with the obstacles will act as heat sources, while the goal point will be the heat sink, pulling the heat closer until it reaches the goal point.…”

Section: The Heat Transfer Analogy In the Configuration Spacementioning

confidence: 99%

Mobile Robot Path Navigation in Static Indoor Environment via AOR 9-Point Laplacian Iteration Numerical Technique

Ling¹,

Dahalan²,

Saudi³

2020

International Journal of Difference Equations

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Mobile robot path navigation is a crucial subject in robotics research and development. The navigation efficiency of a robot correlates directly with its overall performance. With persistent technological growth, the improvement potentials for autonomous robotic remains vast. The objective of this paper is to investigate the performance of the iteration technique called Accelerated Overrelaxation 9-Point (AOR-9P) Laplacian in enabling path navigation for mobile robots. This technique is a derivation from Laplace's equation which is used to calculate the potential fields in the 2-dimensional configuration space representation of an environment. The robotic path navigations are performed in a simulation called Robot 2D Simulator, written in Delphi Project software. After obtaining the solutions generated through AOR-9P iterative technique, the Gradient Descent Search (GDS) technique is employed to determine the best path for the mobile robot to traverse on. The performance of AOR-9P is examined by comparing the number of iterations needed to complete the navigation process. Results shown that AOR-9P enabled path navigation requires the least number of iterations to complete, thus having better performance than its predecessor techniques. In the same time, the paths produced are generally smooth and unobstructed all the way towards the goal point. For future improvements, it is recommended that the Half-Sweep (HS) and Quarter-Sweep (QS) approach to be introduced on AOR-9P iteration technique to improve its performance in solving the mobile robot path navigation problem.

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Path Planning for Mobile Robot using 4EGSOR via Nine-Point Laplacian (4EGSOR9L) Iterative Method

Cited by 13 publications

References 19 publications

An unconditionally stable implicit difference scheme for 2D porous medium equations using four-point NEGMSOR iterative method

An unconditionally stable implicit difference scheme for 2D porous medium equations using four-point NEGMSOR iterative method

A Path Planning Algorithm for a Dynamic Environment Based on Proper Generalized Decomposition

Mobile Robot Path Navigation in Static Indoor Environment via AOR 9-Point Laplacian Iteration Numerical Technique

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