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Proportional Derivative (PD) Control on the Euclidean Group 
Abstract 
In this paper we study the stabilization p … In this paper we study the stabilization problem for control systems
defined on SE(3), the Euclidean group of rigidbody motions.
Assuming one actuator is available for each degree of freedom, we
exploit geometric properties of Lie groups (and corresponding Lie
algebras) to generalize the classical PD control in a coordinatefree
way. For the SO(3) case, the compactness of the group gives rise to a
natural metric structure and to a natural choice of preferred control
direction: an optimal (in the sense of geodesic) solution is given to
the attitude control problem. In the SE(3) case, no natural metric is
uniquely defined, so that more freedom is left in the control design.
Different formulations of PD feedback can be adopted by extending the
SO(3) approach to the whole of SE(3) or by breaking the problem into a
control problem on SO(3) x R^3. For the simple SE(2) case,
simulations are reported to illustrate the behavior of the different
choices. Finally, we discuss the trajectory tracking problem and show
how to reduce it to a stabilization problem, mimicking the usual
approach in R^n. blem, mimicking the usual
approach in R^n. +


Authors  Francesco Bullo and Richard Murray + 
Flags  NoRequest + 
ID  1994n + 
Source  1995 European Control Conference (Rome) + 
Tag  bm95ecc + 
Title  Proportional Derivative (PD) Control on the Euclidean Group + 
Type  Conference paper + 
Categories  Papers 
Modification date This property is a special property in this wiki.

15 May 2016 06:20:42 + 
URL This property is a special property in this wiki.

http://www.cds.caltech.edu/~murray/preprints/bm95ecc.pdf + 
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Proportional Derivative (PD) Control on the Euclidean Group +  Title 
