Development and validation of a linear recursive “Order- N” algorithm for the simulation of flexible space manipulator dynamics

Abstract

Robotic manipulators designed to operate on-board spacecraft and Space Stations are characterized by large spatial dimensions. The structural flexibility inherent in such manipulators introduces a noticeable and undesirable modification of the traditional rigid-body manipulator dynamics. As a result, the dynamics of the complete system comprising a flexible spacecraft or Space Station as a manipulator base, and an attached flexible manipulator, are also modified. Operational requirements related to high manoeuvre accuracy and modest manoeuvre duration, create the need for careful modelling and simulation of the dynamics of such systems. The objective of this paper is to outline the development and validation of an advanced algorithm for the simulation of the dynamics of such flexible spacecraft/space manipulator systems. The requirements imposed during the development of the present prototype dynamics simulator led to the modification and implementation of an existing linear recursive algorithm (“Order- N” algorithm), which requires a computational effort proportional to the number of component bodies in the system. Starting with the Lagrange form of the d'Alembert principle, we first deduce a parametric form which is found to yield—amongst others—the basic forms of the Newton-Euler, the d'Alembert and the Gauss dynamics principles. It is then shown how the application of each of the latter three principles can be made to lead graciously to the desired Order- N algorithm for the flexible multi-body system. The Order- N algorithm thus obtained and validated analytically, forms the basis for the prototype simulator REALDYN, designed to permit numerical simulation of the algorithm on UNIX workstations. Verification, numerical integration and further validation tests have been carried out. Some of the results obtained during the validation exercises could not be explained readily, even in the case of simple multi-body systems. The use of test tools and physical analysis helped resolve those cases. Certainly, the validation of flexible multi-body dynamics algorithms is not entirely straightforward, requiring experience in multi-body dynamics, structural dynamics and numerical simulator development.