Inverse Dynamics of Flexible Robots; Modeling and Recursive Computation Using Virtual Rigid Link Coordinate Systems

Compact Lagrangian formulation of inverse dynamics of flexible arms and its recursive computation algorithm are presented. First, special moving coordinate systems are introduced in order to describe equations of motion in a compact form, which is suited for the formulation of inverse dynamics. Linearization and simplification of the equations of motion are discussed, and the validity and limit of the simplified model are addressed. It is shown that there exist critical speeds of joints at which centrifugal effects are too prominent to neglect the nonlinearity. A closed-form inverse dynamics equation is then derived from the simplified model. For the closed-form equation, which is in a special form, an efficient recursive algorithm for solving the inverse dynamics problem is developed.