Motion Laws Development of Trolley Movement and Tower Crane Slewing

Abstract

The article presents an approach that allows to calculation optimal trajectory of load movement in the building yard. This trajectory provides avoiding obstacles in a way, that ensures the smoothness of the load movement. The essence of the developed approach is in multiple recalculations of the trajectory: the first step brings the shortest path from the initial point to the final point and the obstacle point is in the connection of two parts of the trajectory; the second stage provides changing the second part of the trajectory by a smooth (polynomial) law, that is connected with the first part at the angle 180 degrees; the third stage allows to add acceleration and deceleration modes of motion to the trajectory and reduces the load velocity when it goes near obstacle point. All of the calculations are carried out in an analytical way, and example of numerical calculations is presented in the article as well. In order to make the needed calculation for shifting and rotation of the smooth part of the trajectory (second stage of calculation) all the path was converted into discreet form. Mentioned operation of rotation was carried pot with a rotation matrix. In order to calculate discreet values of mechanisms' velocities the modified digital Savitzky-Golay filter was applied. The output results may be implemented by means of varied frequency drives of the mechanisms. The article ends with comparing of numerical indicators, which refer to the three stages. Among them are: gaps in the velocity of a mechanism during acceleration and deceleration, the gap in the velocity of a mechanism during obstacle avoidance, and the change in velocity sign of a mechanism. All of the indicators were calculated for both of the mechanisms: tower crane slewing and trolley movement. Comparison of the numerical indicators allowed us to conclude, that the final stage (calculations iteration) is the best among the comparable. However, it has some disadvantages, that need to be fixed in further investigations in this direction.