MULTIBODY DYNAMICS 2007, ECCOMAS Thematic Conference

A methodology for the formulation of dynamic equations of motion of a serial flexible-link manipulator using the decoupled natural orthogonal complement (DeNOC) matrices, introduced elsewhere for rigid links, is presented in this paper. First, the Euler Lagrange (EL) equations of motion of the system at hand are written. Then, using the DeNOC matrices associated with the velocity constraints of the connecting bodies a set of recursive expressions for the elements of the associated matrices and vectors are obtained. The expressions also allow one to obtain a recursive forward dynamics algorithm not only for rigid link manipulators, as reported earlier, but also for the flexible link manipulators. In contrast to a serial-chain robot with n rigid links which can have O(n) forward dynamics algorithm, the one proposed here for the n flexible link has an order of O(n)+O(m 3 /3) — m being the maximum number of modes considered for the modeling of beam deflections — complexity. Simulation results for the 3-link Canadarm, considering all its links flexible are reported here, using the proposed algorithm. The numerical stability and efficiency of the proposed algorithm are also investigated, with respect to the Canadarm. 1 INTRODUCTION Research on robotic systems with flexible links started in the international arena in early 1970s. A comprehensive review of various techniques on the modeling of robot-link flexibility is given in [1]. The techniques are principally distinguished as Euler-Lagrange (EL) and Newton-Euler (NE) formulations. The EL formulation requires the successive differentiation of the Lagrangian function of the kinetic and potential energies of the system at hand. Such differentiations are very complex for large multibody systems. Hence, researchers tend to avoid this approach to develop efficient algorithms. As a result, many efficient algorithms for robot dynamics are based on the NE formulation, as given in [2], and others. However, as shown in [3] for rigid-link robots, there is no fundamental difference in the computational complexity of the algorithms based on the EL and NE formulations. The computational efficiency using the NE formulation is apparently visible due the recursive structure in the associated expressions. Hence, the NE formulations are generally preferred by the researchers. Besides the appropriate choice of dynamic formulation methodology, viz. EL or NE, to achieve better computational efficiency of a flexible link robot, selection of proper kinematic model to express the link deflection is also very crucial. Different researchers have used different methods for the kinematic description …