Springer Handbook of Robotics: Chapter 13

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 in 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, 13.1 Robots with Flexible Joints .................... 288 13.1.1 Dynamic Modeling ....................... 289 13.1.2 Inverse Dynamics ......................... 293 13.1.3 Regulation Control ....................... 296 13.1.4 Trajectory Tracking ....................... 301 13.1.5 Further Reading ........................... 305