Alessandro De Luca and Wayne J. Book
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.
Control experiments for a flexible-joint robot arm
Author Mark Spong
Video ID : 135
This 1989 video is about an experimental single-link arm with an elastic joint moving under gravity, which was developed at the Coordinated Science Lab of the University of Illinois at Urbana. The video illustrates some of the control techniques that are mentioned in the first part of Chap. 11: e.g., computed torque using the rigid model (unstable), feedback linearizing control including elasticity (perfect design), and corrective control based on singular perturbation analysis (and its adaptive version). Reference: F. Ghorbel, J.Y. Hung, M.W. Spong: Adaptive control of flexible joint robots, IEEE Control Syst. Mag. 9(7), 9-13 (1989) doi: 10.1109/37.41450