Issues in the dynamics and control of flexible robot manipulators

Abstract

Issues associated with modeling and control of robots with elastic arms are considered. An approach similar to substructure synthesis is used to model the system, where each link is first modeled independently of the others. The joint displacements are then used as constraints to synthesize the equations of motion. It is shown that the centrifugal stiffening effect is the dominating factor for the overall system behavior. Different approaches are discussed for the control design. The effects of flexibility on the response and on the closed-loop control are examined within the context of an example. N important issue of concern in the control of robots is the difference between the total mass of the manipulator and the mass of the payload. If a robot is compared with the human body, it is easily concluded that the manipulator is very inefficient. An inefficient robot implies low productivity and higher costs. A robot can be made more efficient by reducing the thickness of its arms. The resulting increased flexibility, unless considered properly, reduces pointing accuracies and affects the stability of the payload. Another source of inaccuracy is flexibility of the joints. There is considerable debate in the literature as to which source causes more inaccuracies. This paper is concerned with the modeling and control of manipulators with substantial flexibility in the arms. An approach similar to substructure synthesis is used to model the manipulator, and different control strategies are discussed. The mathematical formulation is applicable to robots with revolute or spherical joints. Several methods of modeling manipulators with elastic joints or with flexible arms exist in the literature.111 Each of the approaches uses a variety of assumptions. For example, Refs. 1-4 consider only the static deflections of the links; Ref. 1 treats the connecting links as massless, and Ref. 4 considers only one flexible bending mode for each link. Refer