Murray: htdb2wiki: creating page for 1994n_bm95-ecc.html

2016-05-15T06:20:42Z

htdb2wiki: creating page for 1994n_bm95-ecc.html

← Older revision		Revision as of 06:20, 15 May 2016
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	\| authors = Francesco Bullo and Richard Murray		\| authors = Francesco Bullo and Richard Murray
	\| title = Proportional Derivative (PD) Control on the Euclidean Group		\| title = Proportional Derivative (PD) Control on the Euclidean Group
	\| source = ~~CDS Technical Report 95-010~~		\| source = 1995 European Control Conference (Rome)
	\| year = ~~1995~~		\| year = 1994
	\| type = ~~CDS Technical Report~~		\| type = Conference paper
	\| funding = ~~NSF~~		\| funding =
	\| url = http://www.cds.caltech.edu/~murray/preprints/~~cds95~~-~~010~~.pdf		\| url = http://www.cds.caltech.edu/~murray/preprints/bm95-ecc.pdf
	\| abstract =		\| abstract =
	In this paper we study the stabilization problem for control systems defined		In this paper we study the stabilization problem for control systems
	on SE(3) (the ~~special~~ Euclidean group of rigid-body motions~~) and its~~		defined on SE(3), the Euclidean group of rigid--body motions.
	~~subgroups.~~ Assuming one actuator is available for each degree of freedom,		Assuming one actuator is available for each degree of freedom, we
	we exploit geometric properties of Lie groups (and corresponding Lie		exploit geometric properties of Lie groups (and corresponding Lie
	algebras) to generalize the classical ~~proportional derivative (~~PD) control		algebras) to generalize the classical PD control in a coordinate--free
	in a coordinate-free way. For the SO(3) case, the compactness of the group		way. For the SO(3) case, the compactness of the group gives rise to a
	gives rise to a natural metric structure and to a natural choice of		natural metric structure and to a natural choice of preferred control
	preferred control direction: an optimal (in the sense of geodesic) solution		direction: an optimal (in the sense of geodesic) solution is given to
	is given to the attitude control problem. In the SE(3) case, no natural		the attitude control problem. In the SE(3) case, no natural metric is
	metric is uniquely defined, so that more freedom is left in the control		uniquely defined, so that more freedom is left in the control design.
	design. Different formulations of PD feedback can be adopted by extending		Different formulations of PD feedback can be adopted by extending the
	~~the~~ SO(3) approach to the whole of SE(3) or by breaking the problem into a		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		control problem on SO(3) x R^3. For the simple SE(2) case,
	reported to illustrate the behavior of the different choices. ~~We also~~		simulations are reported to illustrate the behavior of the different
	discuss the trajectory tracking problem and show how to reduce it to a		choices. Finally, we discuss the trajectory tracking problem and show
	stabilization problem, mimicking the usual approach in R^n~~. Finally,~~		how to reduce it to a stabilization problem, mimicking the usual
	~~regarding the case of underactuated control systems, we derive linear and~~		approach in R^n.
	~~homogeneous approximating vector fields for standard systems on SO(3) and~~
	~~SE(3)~~.
	\| flags = NoRequest		\| flags = NoRequest
	\| tag = ~~bm95b~~-~~cds~~		\| tag = bm95-ecc
	\| id = ~~1995m~~		\| id = 1994n
	}}		}}

Murray: htdb2wiki: creating page for 1995m_bm95b-cds.html

2016-05-15T06:20:30Z

htdb2wiki: creating page for 1995m_bm95b-cds.html

New page

{{HTDB paper
| authors = Francesco Bullo and Richard Murray
| title = Proportional Derivative (PD) Control on the Euclidean Group
| source = CDS Technical Report 95-010
| year = 1995
| type = CDS Technical Report
| funding = NSF
| url = http://www.cds.caltech.edu/~murray/preprints/cds95-010.pdf
| abstract =
In this paper we study the stabilization problem for control systems defined
on SE(3) (the special Euclidean group of rigid-body motions) and its
subgroups. 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 proportional derivative (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. We also
discuss the trajectory tracking problem and show how to reduce it to a
stabilization problem, mimicking the usual approach in R^n. Finally,
regarding the case of underactuated control systems, we derive linear and
homogeneous approximating vector fields for standard systems on SO(3) and
SE(3).
| flags = NoRequest
| tag = bm95b-cds
| id = 1995m
}}

Proportional Derivative (PD) Control on the Euclidean Group - Revision history

Murray: htdb2wiki: creating page for 1994n_bm95-ecc.html

Murray: htdb2wiki: creating page for 1995m_bm95b-cds.html