Linearization and sensitivity functions of dynamic robot models

Abstract

The authors have implemented the computer program Algebraic Robot Modeler (ARM) to generate symbolically the forward solution and complete dynamic robot model for control engineering applications. ARM incorporates the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> -matrix formulation of the Lagrangian (Lagrange-Euler) dynamic robot model. The symbolic formulation of dynamic robot models is extended in two directions: <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> -matrices and the Bejczy theorem are applied to linearize symbolically the Lagrangian dynamic robot model about a nominal trajectory; and a methodology is developed to generate symbolically the trajectory sensitivity models of a manipulator with respect to the kinematic and dynamic link parameters. The classical sensitivity point method is thereby extended to include dynamic robot models. Control engineering applications of the linearized and sensitivity models are described. The properties and structural characteristics of these models are identified, and the computational requirements for their implementation in ARM are estimated. The results are illustrated through the double pendulum.