Three - Dimensional Tunnel Passing Maneuvers of Mobile Robots

In this paper, we consider multiple point masses traversing in a 3-dimensional obstacle-ridden environment made up of cylindrical-shaped obstacles, which will act as tunnels. Each point mass will have different targets and avoiding each other and the cylindrical tunnels in its path. The motion of a robot is bounded within a workspace and its velocities are curtailed for safety reasons. Since the workspace is cluttered with 3-dimensional cylindrical shaped objects, we propose a collision-free path that can lead the mobile robot from the desired starting point to the desired location or target. A complete solution to this problem will use the Minimum Distance Technique (MDT) for the generation of the shortest, smoothest and safest path among all the collision-free paths between the initial position and the target. Here, the minimum distance between the center of the point mass, representing a mobile robot, and the surface wall of the cylinder is calculated; thus, only the avoidance of a point on the surface wall of the cylinder is considered. The simulations and derivations are verified by using Mathematica software.