Recursive Algorithms Using Local Constraint Embedding for Multibody System Dynamics

This paper describes a constraint embedding approach for handling of local closure constraints in multibody system dynamics. The approach uses spatial operator techniques to eliminate local-loop constraints from a system to effectively convert it into a tree-topology system. This conversion to a tree-topology allows the direct application of the host of available techniques including mass matrix factorization and inversion to be applied to the system dynamics. One application is the extension of the well-known recursive O(N) forward dynamics for solving the system dynamics of these systems. The algorithms are especially applicable to systems where the constraints are confined to small-subgraphs within the system topology. The paper provides background on the spatial operator approach, the extensions for handling embedded constraints, and concludes with examples of such constraints.