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.
Inverse dynamics control for a flexible link
Author Wayne Book
Video ID : 778
A single flexible link with rotation at its base is controlled by computing the stable inverse dynamics of the flexible system associated with the desired trajectory for the end-effector. This feedforward command is made more robust by the addition of a suitable PD feedback control at the joint. Because of the non-minimum phase nature of the tip output, the resulting input command is non-causal, starting ahead of the actual output trajectory (pre-shaping the link) and ending after (discharging the link). Comparison is made with a PD joint control using a step reference input and with a full state feedback (utilizing strain gauge signals and their rates) and a nominal trajectory command. The inverse dynamics control demonstrates superiority both in terms of overshoot and residual vibrations. References: 1. D.-S. Kwon: An Inverse Dynamic Tracking Control for a Bracing Flexible Manipulator, Dissertation, School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, (1991); 2. D.-S. Kwon, W.J. Book: A time-domain inverse dynamic tracking control of a single-link flexible manipulator, ASME J. Dyn. Syst. Meas. Control 116, 193-200 (1994); doi: 10.1115/1.2899210