Fourier-based optimal design of a flexible manipulator path to reduce residual vibration of the endpoint

Abstract

A method is presented for generating the path which significantly reduces residual vibration. The desired path is optimally designed so that the system completes the required move with minimum residual vibration. The dynamic model and optimal path are effectively formulated and computed by using special moving coordinates, called virtual rigid link coordinates, to represent the link flexibilities. Also joint compliances are included in the model. Characteristics of residual vibration are identified from the linearized equations of motion. From these results, the performance index is selected to reduce residual vibration effectively. The path to be designed is developed by a combined Fourier series and polynomial function to satisfy both the convergence and boundary condition matching problems. The concept of correlation coefficients is used to select the minimum number of design variables, i.e. Fourier coefficients, the only ones which have a considerable effect on the reduction of residual vibration. A two-link manipulator is used to evaluate this method. Results show that residual vibration can be drastically reduced by selecting an appropriate manipulator path.