A skew-symmetric form of the recursive Newton-Euler algorithm for the control of multibody systems

We derive a form of the recursive Newton-Euler algorithm that satisfies the skew-symmetry property M˙-2C=-(M˙-2C)^T required in a variety of nonlinear control laws occurring throughout the field of multibody dynamics. We show that the recently developed formulation of multibody dynamics based on Lie groups can be modified to accommodate the skew-symmetry requirement. Specifically, we demonstrate that explicit block-triangular factorizations of both M and C are embedded within the structure of the recursive algorithm. Furthermore, the factorization of the mass matrix M can be differentiated explicitly with respect to time. The resulting expressions for M, M˙, and C immediately lead to a proof based entirely on high-level matrix manipulations demonstrating the skew-symmetry of M˙-2C