Approximate Modeling of Robots Having Elastic Links

The exact modeling of robots with flexible links is scarcely useful from simulation and/or control points of view. In fact, reflecting the distributed nature of the link flexibility, the exact model is represented by nonlinear partial differential equations. The paper presents a method to derive approximate dynamic models consisting of a system of ordinary differential equations whose order, for a given robot, is related to the desired order of approximation. Such models are obtained by using the Lagrangian approach and by expanding in a limited number of terms the generalized coordinates describing the exact shape of the beams constituting the robot. We give a procedure that allows, if implemented on a computer, the automatic generation of the models. With such a procedure, by using the symbolic language MACSYMA, the models of one and two-link flexible robots have been developed. Simulation tests to validate the proposed approximate model are included. These tests show that satisfactory results in terms of dynamic behavior of the approximate model are obtainable even with a reduced order of approximation. © 1989 IEE