On Feedback Linearization of Robot Manipulators and Riemannian Curvature

  • Mark W. Spong
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 104)


In this paper we discuss the problem of feedback linearization of rigid robot manipulators. We have shown previously that a necessary and sufficient condition for exact linearization of such systems under a nonlinear coordinate transformation in the state and input space is that the Riemannian curvature tensor associated with the robot inertia matrix vanish identically [17]. Moreover the coordinate transformation is given as the solution of an easily characterized system of partial differential equations. We first review the result from [17] and then discuss the idea of approximate feedback linearization, i.e. feedback linearization of a simplified model. Approximate feedback linearization is useful in this context since the class of robots that satisfy the conditions for exact linearizability is limited. We will show a connection between approximate feedback linearization based on Riemannian curvature and both the imaginary robot concept of Gu and Loh [12] and thepassive computed torque of Anderson [3].


Robot Manipulator Feedback Linearization Inertia Matrix Riemannian Curvature Christoffel Symbol 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Mark W. Spong
    • 1
  1. 1.Coordinated Science LaboratoryUniversity of Illinois at Urbana—ChampaignUrbanaUSA

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