Title :
A skew-symmetric form of the recursive Newton-Euler algorithm for the control of multibody systems
Author_Institution :
Jet Propulsion Lab., California Inst. of Technol., Pasadena, CA, USA
Abstract :
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
Keywords :
Lie groups; matrix algebra; motion control; nonlinear control systems; robot dynamics; Lie groups; block-triangular factorizations; mass matrix; multibody systems; nonlinear control systems; recursive Newton-Euler algorithm; recursive algorithm; robotics; skew-symmetric form; Control systems; Equations; Gravity; Laboratories; Nonlinear control systems; Nonlinear dynamical systems; Orbital robotics; Propulsion; Robot kinematics; Symmetric matrices;
Conference_Titel :
American Control Conference, 1999. Proceedings of the 1999
Conference_Location :
San Diego, CA
Print_ISBN :
0-7803-4990-3
DOI :
10.1109/ACC.1999.786211