A symbolic geometric formulation of branched articulated multibody systems based on graphs and lie groups

摘要

In this article we present a symbolic closed-form matrix formulation to obtain the dynamic equations of branched articulated multibody systems (AMS)s. The proposed approach uses geometric mechanics based on Screw Theory and Lie groups. Both Lagrange's and Newton-Euler's equation of motion are derived. Furthermore, the structure of the proposed set of geometric equations holds the intrinsic robot parameters explicitly arranged like symbolic matrices. The formulation is valid for any branched AMS without closed kinematic chains and whose joints have one degree of freedom (DoF) (revolute and/or prismatic). All these properties allow the use of these equations in different algorithms such as identification, simulation and control of branched AMSs like hands or humanoids. Finally, the proposed equations have been validated and verified with the multi-body simulation software package MSC=ADAMS© by computing the inverse dynamics of a two arm torso of 16 DoF.