Intrinsic Observer-Based Stabilization for Simple Mechanical Systems on Lie Groups

• DOI: 10.1137/s0363012904439891
• Publication Date: 2005-12-06T03:29:59Z
• Authors: D. H. S. Maithripala; W. P. Dayawansa; J. M. Berg
• Keywords: Observer (physics); Passivity

This paper presents a dynamic observer for class of simple mechanical systems on Lie groups. provides velocity estimates based configuration measurements. The is \textit{intrinsic}, so its performance does not depend the choice coordinates, and it \textit{coordinate free}, in sense that equations may be written explicitly without specifying coordinates space. Our main result obtained by specializing previous Aghannan Rouchon concerning estimation Riemannian manifolds to such specialization nonobvious extremely powerful. Further we extend original include velocity-dependent external forces. estimator, combined with coordinate-free formulation passivity-based state-feedback control, allows construction coordinate-free, intrinsic output feedback compensator. is, our knowledge, first time has been reported. Explicit expressions are computed groups $SO(3)$ $SE(3)$, allowing easy practical problems rigid body motion. theory illustrated via application axisymmetric top six-degrees-of-freedom microelectromechanical system.