1 Automation & Control, The Faculty of Engineering and Science, Aalborg University, VBN2 Department of Electronic Systems, The Faculty of Engineering and Science, Aalborg University, VBN3 Aalborg University Space Center, The Faculty of Engineering and Science, Aalborg University, VBN4 unknown
|If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system afected by an external force of a control action. Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincare reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modeling, estimation and control of mechanical systems. A control system generates an external force, which may break the symmetry in the dynamics. This paper shows how to model and to control a mechanical sys- tem on the reduced phase space, such that complete state space asymptotic stabilization can be achieved. The paper comprises a specialization of the well-known Euler-Poincare reduction to a rigid body motion with forcing.
Proceedings of Methods and Models in Automation and Robotics, 2005
Control of Mechanical Systems; Differential Geometric Methods; Attitude Control; Nonlinear Control
Main Research Area:
Methods and Models in Automation and Robotics, 2005