DEVELOPMENT AND VALIDATION OF A LINEAR RECURSIVE ORDER-N ALGORITHM FOR THE SIMULATION OF FLEXIBLE SPACE MANIPULATOR DYNAMICS

Robotic manipulators designed to operate on-board spacecraft and Space Stations are characterized by large spatial dimensions. The structura l flexibility inherent in such manipulators introduces a noticeable an d undesirable modification of the traditional rigid-body manipulator d ynamics. As a result, the dynamics of the complete system comprising a flexible spacecraft or Space Station as it manipulator base, and an a ttached flexible manipulator, are also modified. Operational requireme nts related to high manoeuvre accuracy and modest manoeuvre duration, create the need for careful modelling and simulation of the dynamics o f such systems. The objective of this paper is to outline the developm ent and validation of an advanced algorithm for the simulation of the dynamics of such flexible spacecraft/space manipulator systems. The re quirements imposed during the development of the present prototype dyn amics simulator led to the modification and implementation of an exist ing 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 prin ciple, we first deduce a parametric form which is found to yield-among st others-the basic forms of the Newton-Euler, the d'Alembert and the Gauss dynamics principles. It is then shown how the application of eac h of the latter three principles can be made to lead graciously to the desired Order-N algorithm for the flexible multi-body system. The Ord er-N algorithm thus obtained and validated analytically, forms the bas is for the prototype simulator REALDYN, designed to permit numerical s imulation of the algorithm on UNIX workstations. Verification, numeric al integration and further validation tests have been carried out. Som e 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. C ertainly, the validation of flexible multi-body dynamics algorithms is not entirely straightforward, requiring experience in multi-body dyna mics, structural dynamics and numerical simulator development.