Robots with flexible elements

Design issues, dynamic modeling, trajectory planning, and feedback control problems are presented for robot manipulators having components with mechanical flexibility, either concentrated at the joints or distributed along the links. The chapter is divided accordingly into two main parts. Similarities or differences between the two types of flexibility are pointed out wherever appropriate. For robots with flexible joints, the dynamic model is derived in detail by following a Lagrangian approach and possible simplified versions are discussed. The problem of computing the nominal torques that produce a desired robot motion is then solved. Regulation and trajectory tracking tasks are addressed by means of linear and nonlinear feedback control designs. For robots with flexible links, relevant factors that lead to the consideration of distributed flexibility are analyzed. Dynamic models are presented, based on the treatment of flexibility through lumped elements, transfer matrices, or assumed modes. Several specific issues are then highlighted, including the selection of sensors, the model order used for control design, and the generation of effective commands that reduce or eliminate residual vibrations in rest-to-rest maneuvers. Feedback control alternatives are finally discussed. In each of the two parts of this chapter, a section is devoted to the illustration of the original references and to further readings on the subject.