Path planning of mobile robots in dynamic environment based on analytic geometry and cubic Bézier curve with three shape parameters

With the improvement of technology, autonomous mobile robots have become an indispensable part of human life. Since path planning is the crucial part of mobile robots, these paths should be feasible, smooth and collision-free in a certain environment. However, forming desirable paths in a dynamic environment with static and moving obstacles is still a problem in the literature. In this paper, we present a new approach based on the analytic geometry for collision avoidance and the cubic Bézier curve with three shape parameters to obtain global and local paths in a dynamic environment. In this study, the environment for the mobile robot is considered to be a square plane without a grid consisting of several static obstacles in different geometric shapes, a mobile robot, and several dynamic obstacles in the shape of a circle with the same size. Moreover, we expressed the influence of the shape parameters on the optimal path using the objective function defined by the path length. Also, the paths generated by the cubic Bézier curve with three shape parameters and the classical cubic Bézier curve are compared in terms of their path length.