Variable-Gain Constraint Stabilization for General Multibody Systems with Applications

Abstract

This paper presents a general and efficient formulation applicable to a vast variety of rigid and flexible multibody systems. It is based on a variable-gain error correction with scaling and adaptive control of the convergence parameter. The methodology has the following distinctive features. (i) All types of holonomic and non-holonomic equality constraints as well as a class of inequalities can be treated in a plain and unified manner. (ii) Stability of the constraints is assured. (iii) The formulation has an order Ncomputational cost in terms of both the constrained and unconstrained degrees of freedom, regardless of the system topology. (iv) Unlike the traditional recursive order Nalgorithms, it is quite amenable to parallel computation. (v) Because virtually no matrix operations are involved, it can be implemented to very simple general-purpose simulation programs. Noting the advantages, the algorithm has been realized as a C++ code supporting distributed processing through the Message-Passing Interface (MPI). Versatility, dynamical validity and efficiency of the approach are demonstrated through numerical studies of several particular systems including a crawler and a flexible space structure.