Robotic Path: Analysis of Algebraic Topological Properties of Stream Lines Due to Source-Sink, Dipole and Vortex

Abstract

The importance of robotic path planning cannot be overstated. Robotic path planning plays a crucial role in ensuring efficient and safe navigation for robots. It enables robots two autonomously determine the most optimal path to reach their destination while avoiding of obstacles and potential collisions. By carefully analyzing the environment and considering various factors such as distance, speed, and obstacles, robotic path planning enhances the overall performance and productivity of robots. Moreover, it minimizes the risk of accidents and damage to both the robots and their surroundings. In industries such as manufacturing logistics and health care where robots are extensively used, effective path planning is essential for seamless operations and improved efficiency. Therefore, investing in advance robot planning terms and technology is crucial to unlock the full potential of robotics and automation Due to ubiquity and exquisite properties: source, sink, dipole and vortex are central concepts in fluid mechanics and hence the fluid flows are outright concurrent with it. Source and sink in tandem manifest the crucial properties. Thus, the discussion pervades in almost every branch of science, tempted the researcher and compel to work. One such attempt is made in this paper, to study the algebraic topological properties like homotopy, null homotopy and fundamental group of stream lines of flow due source-sink, dipole and vortex which can render analytic simulation of natural phenomenon as well as robotic path planning.