Implicit finite element formulation of the inverse dynamics of vibrating robots

Inverse dynamics methods have a high potential for the design of feedforward controllers for flexible robots. In this work, a general finite element framework is proposed for the formulation of the inverse dynamics problem, which can account for the flexibility in the links and joints and for arbitrary mechanical topologies, e.g., including closed kinematic loops. The dynamics between the joint torques and the tip motion of a flexible manipulator is generally not minimum-phase, however, practical inverse dynamics solutions can be obtained based on the formulation of a two-point boundary value problem or an optimization problem. The proposed methodology is illustrated for the feedforward control of a parallel kinematic delta robot with three flexible links.