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Properties of the Dynamic Equations in Matrix Form

  • Pål Johan From
  • Jan Tommy Gravdahl
  • Kristin Ytterstad Pettersen
Part of the Advances in Industrial Control book series (AIC)

Abstract

When deriving the dynamic equations of mechanical systems it is common to present the equations in matrix form in such a way that the different matrices, in particular the inertia and Coriolis matrices, possess certain properties. These properties are very useful when deriving control laws and in the stability proofs of these. The most important properties in robotics are the boundedness property of the inertia matrix and the skew symmetry property of the Coriolis matrix.

For both these properties vehicle-manipulator systems need to be treated differently from standard fixed-base manipulators or single rigid bodies. This has led to several misconceptions in the robotics literature, because these properties are often taken for granted for vehicle-manipulator systems based on the proofs of other systems. This chapter therefore shows when these properties are in fact true for vehicle-manipulator systems, and for what formulations of the dynamics they are not.

Keywords

Multibody System Model Predictive Control Robotic Manipulator Inertia Matrix Christoffel Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Pål Johan From
    • 1
  • Jan Tommy Gravdahl
    • 2
  • Kristin Ytterstad Pettersen
    • 2
  1. 1.Department of Mathematical Sciences and TechnologyNorwegian University of Life SciencesÅsNorway
  2. 2.Department of Engineering CyberneticsNorwegian Univ. of Science & TechnologyTrondheimNorway

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