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.
Input shaping on a lightweight gantry robot
Author Wayne Book
Video ID : 777
This video shows an industrial application by CAMotion, Inc. of input command shaping to cancel modes of vibration of a large, lightweight gantry robot, designated the LDP, carrying a heavy “log” of printed paper to a conveyor. The method has been patented (D.P. Magee, W.J. Book: Optimal Arbitrary Time-delay (OAT) Filter and Method to Minimize Unwanted System Dynamics, US Patent 6078844 (2000)). This commercial robot is the one depicted also in Fig. 11.13. Its successor is marketed by PaR Systems, Inc. Reference: D.P. Magee, W.J. Book: The application of input shaping to a system with varying parameters, Proc. 1992 Japan-USA Symp. Flexible Automation, San Francisco (1992), pp. 519-526