View source for Proportional Derivative (PD) Control on the Euclidean Group

{{HTDB paper
| authors =  Francesco Bullo and Richard Murray 
| title = Proportional Derivative (PD) Control on the Euclidean Group
| source = 1995 European Control Conference (Rome)
| year = 1994
| type = Conference paper
| funding = 
| url = http://www.cds.caltech.edu/~murray/preprints/bm95-ecc.pdf
| abstract = 
In this paper we study the stabilization problem for control systems
defined on SE(3), the Euclidean group of rigid--body 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 coordinate--free
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.
| flags = NoRequest
| tag = bm95-ecc
| id = 1994n
}}