Optimal mode movement of the robot manipulator on an elastic base according to the criterion of the mean square value of the acceleration of the drive torque

Abstract

Previous studies of the optimization of the manipulator motion mode on an elastic base based on the criteria of the rms value of the drive torque and the rate of change of the rms value of the drive torque established that the use of optimal manipulator motion modes, which are created on the basis of higher derivatives of the characteristics of the change of the drive torque, allow to obtain more smooth movements of the boom system of the manipulator, thereby reducing its oscillations on the elastic support. At the same time, the obtained optimal modes of movement didn't completely eliminate the boom system oscillations during the change of departure. By observing the oscillations of the elastic link of the manipulator, the quality of the obtained optimal modes of movement was evaluate and the presence of residual oscillations was shown.
 This work considers the possibility of optimizing the manipulator's motion mode based on the criterion of the mean square value of the acceleration of the drive torque change. For this purpose, the second derivative of the driving torque function of the manipulator boom system drive was determined first. Such a criterion for optimizing the motion mode is an integral functional, the minimization of which is carry out by the methods of variational calculus. The regularity of the change of the driving torque it was find from the dynamic equation of motion.
 The search for the optimal motion mode of the manipulator realized through the solution of the Poisson boundary nonlinear differential equation of the fourth order.
 The results of the conducted research made it possible to clarify much better the nature of the vibrations of the manipulator boom system and, as a result, to develop a drive control system that allows the realization of the obtained optimal mode of movement.