Singular Perturbation Analysis of a Distributed Parameter Model of Flexible Manipulators

The effect of flexure on the rigid body motion of flexible link manipulators is considered through singular perturbation methods. It is shown that the dynamics of flexible manipulators can be resolved into rigid and flexible modes when a small parameter embedded in the model vanishes. The coupling of the flexure and the rigid modes is investigated by appealing to the higher order terms in the expansion. The model used is the nonlinear integropartial differential equation resulting from the extended Hamiltonian principle. Analysis of this model yields more insight and simplifies generation of the higher order terms that represent the coupling between the rigid and the flexure modes as compared to a finite-dimensional approximation of the model. Finally, asymptotic perturbation techniques are utilized to generate a composite control law.