Geometric numerical integration algorithms for articulated multi-body systems

Numerical integration methods based on Lie group theoretic geometrical approaches are extended to articulated multi-body systems with rigid body displacements belonging to the special Euclidean group SE (3) as a part of generalized coordinate. Two Lie group integrators, Crouch-Grossman method and Munthe-Kaas method, are formulated for the equation of motion for articulated multi-body systems. The proposed methods provide singularity-free integration, unlike the Euler-angle method, while the integration always evolves on the underlying manifold structure, unlike the quarternion method. Numerical simulation result validates the methods by checking energy and momentum conservation at even integrated system state.