Recursive derivation of explicit equations of motion for efficient dynamic/control simulation of large multibody systems

Abstract

The demands of spacecraft, robot, and machinery design have motivated the development of general purpose multibody computer programs for dynamic analysis. Such programs enable the analyst to simulate, with minimal manual effort, motions of large systems of rigid bodies, or to calculate the control forces and torques which must be applied to obtain a desired motion of such systems. Multibody programs tend to be plagued by two basic inefficiencies. The first, and most severe, arises from computational requirements associated with the determination of state derivative values. If n is the number of degrees of freedom of a system, the number of computational operations required to calculate state derivative values tends to be a cubic function in n, and thus can become prohibitively large for even modest values of n. The second inefficiency manifests itself when equations are derived for the most general system, as they frequently are. Such implicit programs generally are replete with unnecessary computations or logical statements. Presented here is an approach which does not suffer from either of these deficiencies. State derivative values are calculated in a highly efficient manner, the number of computational operations being a linear function in n. Problem specific equations are generated through the use of symbolic manipulation, which yields explicit equations devoid of needless operations. Finally, the equations are cast in a highly concurrent form, allowing the production of a simulation code that can be used on conventional sequential computers, but is well suited for parallel computers with distributed architecture.