An Inverse Jacobian Solution for the Control of Multi-link Flexible Manipulators

In this paper, an inverse Jacobian solution is presented for a multi-link flexible manipulator. This solution yields quick endpoint control of flexible manipulators that are modeled as a series of finite elements. The model is partitioned into links connected by passive (nonactuated) and active (actuated) joints. This partitioned structure is maintained in the development of the kinematics and dynamics of the multi-link flexible manipulator. After some rearrangement of the matrix blocks, an application of the matrix inversion lemma, and an application of a fast recursive inversion of mass and Jacobian matrices developed for rigid link manipulators, the final inverse Jacobian solution is obtained.