Dynamic modeling method for constrained system with singular mass matrices

The dynamic model is beneficial for system control design, especially when it is related to precise force adjustment. Traditional modeling methods make it difficult to address multi-body systems with singular mass matrices or are computationally expensive. In this paper, an approach termed the Extended Rosenberg Embedding Method for dynamic modeling is presented. By incorporating the constraints directly into the Fundamental Equation, the proposed approach enables the description of the system motion in two separate equations, which can reduce the computational cost of the constrained dynamic model. This method provides a new way to establish motion equations, regardless of whether the system is subject to holonomic or non-holonomic constraints. Moreover, as the method does not impose direct requirements on the rank of the mass matrix, it is capable of handling the modeling of multi-body systems with singular mass matrices. The validity of the proposed method is substantiated through rigorous mathematical derivation, while its accuracy and computational efficiency are corroborated through the examination of two numerical examples.