Prediction of the dynamic response of flexible manipulators from a modal database

Presented in this work is a modal-data-based and experimentally-orientated method to predict the dynamic response of a time-varying and non-linear system, consisting of a robot manipulator with elastic members. The method utilizes modal models which can be reliably obtained through well-known modal testing techniques. For such a system where modal characteristics vary with robot position or time, modal testing usually yields modal data in a limited number of positions. In order to employ these data, which may be coarsely placed in a robot's workspace, an interpolation technique is used to obtain continuous modal variations. These interpolated modal data along with the mass properties are utilized to form a modal summation solution for prediction of the time history of deformable motion. This approach is more efficient since the modal database identified for a robot can be repeatedly used for a variety of different tasks. Because modal data can usually be experimentally obtained from modal testing with a great degree of reliability, the prediction on this basis should lead to more accurate time response information. Case studies are conducted for robot trajectory planning of a prismatic-and-revolute manipulator, with primary consideration of elastodynamically-induced positioning inaccuracy.