On Modeling and Control of Flexible Manipulators

Industrial robot manipulators are general-purpose machines used for industrial automation in order to increase productivity, flexibility, and quality. Other reasons for using industrial robots are cost saving, and elimination of heavy and health-hazardous work. Robot motion control is a key competence for robot manufacturers, and the current development is focused on increasing the robot performance, reducing the robot cost, improving safety, and introducing new functionalities. Therefore, there is a need to continuously improve the models and control methods in order to fulfil all conflicting requirements, such as increased performance for a robot with lower weight, and thus lower mechanical stiffness and more complicated vibration modes. One reason for this development of the robot mechanical structure is of course cost-reduction, but other benefits are lower power consumption, improved dexterity, safety issues, and low environmental impact. This thesis deals with three different aspects of modeling and control of flexible, i.e., elastic, manipulators. For an accurate description of a modern industrial manipulator, the traditional flexible joint model, described in literature, is not sufficient. An improved model where the elasticity is described by a number of localized multidimensional springdamper pairs is therefore proposed. This model is called the extended flexible joint model. This work describes identification, feedforward control, and feedback control, using this model. The proposed identification method is a frequency-domain non-linear gray-box method, which is evaluated by the identification of a modern six-axes robot manipulator. The identified model gives a good description of the global behavior of this robot. The inverse dynamics control problem is discussed, and a solution methodology is proposed. This methodology is based on a differential algebraic equation (DAE) formulation of the problem. Feedforward control of a two-axes manipulator is then studied using this DAE approach. Finally, a benchmark problem for robust feedback control of a single-axis extended flexible joint model is presented and some proposed solutions are analyzed.