A Boundary Node Method for path planning of mobile robots

In this paper we propose a new method for solving the path planning problem in a static environment to find an optimal collision-free path between starting and goal points. First, the grid model of the robot's working environment is constructed, and then the potential value of the grid cells is calculated based on the new proposed potential function. This function is used to guide the robot to move toward the desired goal, it has the lowest value at the goal position and the value is increased as the robot moves further away. Second, we developed an efficient method, called the Boundary Node Method, to find the initial feasible path. In this method, the robot is simulated by a nine-node quadrilateral element, where the centroid node represents the robot's position. The robot moves in the working environment toward the goal with eight-boundary nodes based on the potential value of the boundary nodes. The initial feasible path is generated from a sequence of waypoints that the robot has to traverse as it moves toward the goal point without colliding with any obstacles. However, the proposed method can generate the path safely and efficiently, but the path is not optimal in terms of the total path length. Therefore, in order to construct an optimal or near-optimal collision-free path, an additional method, called the Path Enhancement Method, is developed. Finally, the cubic spline interpolation is adopted to generate a continuous smooth path that connects the starting point to the goal point. The proposed method has been tested in several working environments with different degrees of complexities. The results demonstrated that the proposed method is able to generate near-optimal collision-free path efficiently. Moreover, we compared the performance of the proposed methods with the other path planning methods in terms of path length and computational time. The results revealed that the proposed method can solve the robot path planning problem more efficiently. Finally, in order to verify the performance of the developed method for generating a collision-free path, experimental studies were carried out on the real robot.