Abstract
Mobile robots are always in a state where they have to find a collision-free path in their environment from start to the target point. This study tries to solve the problem of mobile robot iteratively by using a numerical technique. It is based on potential field technique that was modelled using the Laplace’s equation to restrain the creation of a potential functions across regions in the mobile robot’s configuration space. The gradient formed by the potential field is then used to generate a path for the robot to advance through. The present paper proposes a Two-Parameter Over-Relaxation (TOR) iterative method that is used to solve Laplace’s equation for obtaining the potential field that is then utilized for finding path of the robot, thus solving the robot pathfinding problem. The experiment indicates that it is capable of producing a smooth path between the starting and target points through the use of a finite-difference technique. Furthermore, the simulation results show that this numerical approach executes quicker and provides a smoother trail than to the previous works, that includes Successive Over-Relaxation (SOR) and Accelerated Over-Relaxation (AOR) methods.
Highlights
Pathfinding or navigation problem plays an important role in autonomous mobile robots
This paper aims to simulate a point-robot pathfinding in the configuration space using numerical potential functions based on heat transfer theory
This experiment reveals that the solution of robot pathfinding problems via numerical approaches is very smart and practicable, by reason of the recent advancements and newly emerging techniques, along with the accessibility of fast machines in present day
Summary
Pathfinding or navigation problem plays an important role in autonomous mobile robots. This paper aims to simulate a point-robot pathfinding in the configuration space using numerical potential functions based on heat transfer theory. The problem of heat transfer in this study is posed as Laplace’s equation. Laplace’s equation solutions better recognized as harmonic functions, mathematically describe the temperature values for the path generation model in the configuration space. There have been different approaches used to obtain harmonic functions but, by reason of the obtainability of fast processing machines and their elegance and competence in resolving the problem, the most general approach is via numerical techniques. Three experiments were carried out to investigate the efficiency of the accelerated iterative method used in producing paths of a mobile robot for multi-size environments
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