An algorithm that presents the best possible approximation for the theoretical Bézier curve and the real path on which a mobile robot moves in a dynamic environment with mobile obstacles and boundaries is introduced in this paper. The algorithm is tested on a set of scenarios that comprehensively cover critical situations of obstacle avoidance. The selection of scenarios is made by deploying robot navigation performances into constraints and further into descriptive characteristics of the scenarios. Computer-simulated environments are created with dedicated tools (i.e., Gazebo) and modeling and programming technologies (i.e., Robot Operating System (ROS) and Python). It is shown that the proposed algorithm improves the performance of the path for robot navigation in a highly dynamic environment, with dense mobile obstacles.