Existence and uniqueness of solutions of the inverse dynamics of multilink flexible arms: Convergence of a numerical scheme

The inverse dynamics of flexible manipulators consists in finding the joint torques that drive the end effector of a manipulator along a given trajectory. A proof of the existence and uniqueness of solutions of the inverse dynamics of planar open-chain multilink flexible manipulators and the convergence of an algorithm previously proposed by the second author for the numerical solution of the problem are presented in this article. Higher-order strain terms leading to the geometric stiffness matrix in finite element models are included in the formulation and their influence on the inverse dynamics solution is studied.