Multibody formalism for real-time application using natural coordinates and modified state space

摘要

The paper describes the multibody formalism based on natural coordinates and modified state space that is suitable for real-time applications. The complex multibody systems include closed loops and thus result into DAE equations. Their simulation then usually requires iterative stabilization. The described multibody formalism has two important properties making it suitable for real-time applications. Firstly, it provides the stable solution of DAE equations for multibody systems with kinematical loops without necessity of iterations. Secondly, it consists of system matrices with simple expressions (constant, linear or quadratic terms) for their elements and thus it is very suitable for massive parallelization. The resulting computational complexity is growing only linearly with the number of DOFs despite any occurrence of kinematical loops and it is about 5 times smaller than the recursive multibody formalisms.