Dynamic Analysis of Robot Manipulators: A Cartesian Tensor Approach(131 The Springer International Series in Engineering and Computer Science)

The purpose of this monograph is to present computationally efficient algorithms for solving basic problems in robot manipulator dynamics. In par­ ticular, the following problems of rigid-link open-chain manipulator dynam­ ics are considered : i) computation of inverse dynamics, ii) computation of forward dynamics, and iii) generation of linearized dynamic models. Com­ putationally efficient solutions of these problems are prerequisites for real­ time robot applications and simulations. Cartesian tensor analysis is the mathematical foundation on which the above mentioned computational algorithms are based. In particular, it is shown in this monograph that by exploiting the relationships between second order Cartesian tensors and their vector invariants, a number of new tensor­ vector identities can be obtained. These identities enrich the theory of Carte­ sian tensors and allow us to manipulate complex Cartesian tensor equations effuctively. Moreover, based on these identities the classical vector descrip­ tion for the Newton-Euler equations of rigid body motion are rewritten in an equivalent tensor formulation which is shown to have computational advan­ tages over the classical vector formulation. Thus, based on Cartesian tensor analysis, a conceptually simple, easy to implement and computationally efficient tensor methodology is presented in this monograph for studying classical rigid body dynamics. XlI Application of this tensor methodology to the dynamic analysis of rigid-link open-chain robot manipulators is simple and leads to an efficient fonnulation of the dynamic equations of motion.

Table of Contents:
1 Introduction.- 1.1 Basic Problems in Robot Manipulator Dynamics.- 1.2 General Remarks on Robot Manipulator Dynamics.- 1.3 Objectives and Motivation.- 1.4 Preview.- 1.5 References.- 2 Notation, Terminology and Background Material.- 2.1 Notation.- 2.2 Rigid Bodies and their Finite Displacement.- 2.3 Robot Manipulators.- 2.4 References.- 3 Cartesian Tensor Analysis.- 3.1 Introduction.- 3.2 Second Order Cartesian Tensors.- 3.3 Properties of Second Order Cartesian Tensors.- 3.4 Cartesian Tensor Algebraic Identities.- 3.5 References.- 4 Cartesian Tensors and Rigid Body Motion.- 4.1 Introduction.- 4.2 On Kinematic Analysis of Rigid Body Motion.- 4.3 On Dynamic Analysis of Rigid Body Motion.- 4.4 References.- 5 Manipulator Inverse Dynamics.- 5.1 Introduction.- 5.2 Previous Results and General Observations on Manipulator Inverse Dynamics.- 5.3 A Cartesian Tensor Approach for Solving the IDP.- 5.4 The Use of Euler-Lagrange and Kane’s Formulations in Deriving Algorithm 5.7.- 5.5 Concluding Remarks.- 5.6 References.- 6 Manipulator Forward Dynamics.- 6.1 Introduction.- 6.2 Previous Results on Manipulator Forward Dynamics.- 6.3 The Generalized Manipulator Inertia Tensor.- 6.4 Implementation and Computational Considerations.- 6.5 Concluding Remarks.- 6.6 References.- 7 Linearized Dynamic Robot Models.- 7.1 Introduction.- 7.2 Linearization Techniques.- 7.3 Joint Space Linearized Dynamic Robot Models.- 7.4 Cartesian Space Robot Dynamic Models and their Linearization.- 7.5 Concluding Remarks.- 7.6 References.- A Recursive Lagrangian Formulation.- B On Moment Vectors and Generalized Forces.- C On Partial Differentiation.- D List of Symbols and Abbreviations.