Algorithms for Planning Trajectory of a Modular Wheeled In-pipe Robot

Abstract

The 2D and 3D mathematical and computer models of the kinematics of a modular wheeled robot when it moves inside the pipe for inspection of the inner surface are presented in this paper. In the 2D model the transition of the leading module from a linear trajectory to an arc with a constant radius and subsequent exit to a straight trajectory is considered. A numerical algorithm for the driven modules motion based on the position of the leading module and the constraint equation is constructed. As the analysis results of the simulation data, the dependence of the deviation between leading and driven modules trajectories versus the radius of the curved section is revealed. The optimal trajectory of the robot movement inside the curved pipe is synthesized in which all modules
remain within the safety zone, considering the deviations of the modules from the trajectory of the first one. An analytical 3D model is obtained which allows calculating the following movements: along the helical line trajectory (working mode of pipe inspection); dynamic change in the pitch of the helix; transition to movement along the circumference or along the pipe. The deviations of the tra-
jectory of the driven modules from the trajectory of the leading module are analyzed and structural methods of reducing the magnitude of these deviations are proposed. Computer models were coded with the C++ and Python programming languages. The visualization of the modular robot movement was carried out by the 3D modeling software Blender.