Planning the optimal trajectory of the robot-machine parallel structure

Abstract

The article considers the task of a tripod robot controlling, which includes two related subtasks: planning the optimal trajectory of motion and its implementation. The realization of the chosen trajectory of motion is carried out by standard methods of control theory and was considered earlier by the authors. Trajectory of the robot’s movement is largely determined by the assigned tasks. Movement of the output link include, firstly, working displacements for the purpose of machining the product and are completely determined by the surface of the workpiece. Secondly - positioning, i.e. the tool movement to the beginning of the next stage of processing. In this case, the motion can be relatively free in some arbitrary trajectory, taking into account the limitations determined by the working area of the mechanism and the surface of the workpiece. For a planar 3RPR robot, the input coordinates are the lengths of the drive links. The output coordinates of the robot (workspace) are limited by the range of permissible lengths of the drive links and the Jacobian sign-sign region. For the obtained working space of the planar 3RPR robot, in the coordinates (11, 12, 13) additional restrictions are introduced, related to the dimensional dimensions of the workpiece. It is shown that the direct use of the Chebyshev metric as an objective function to optimize the positioning path is inexpedient, since Chebyshev’s metric makes a significant ambiguity in the choice of the trajectory. To this end, it is proposed to supplement the original objective function with the Euclidean metric taken with some small weighting coefficient. Optimization was carried out with restrictions on the size of the working space and the workpiece. The results of mathematical modeling are presented.