Difference between revisions of "Control on the Sphere and Reduced Attitude Stabilization"

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{{HTDB paper
 
{{HTDB paper
| authors =  Francesco Bullo, Richard M. Murray and Augusto Sarti  
+
| authors =  Francesco Bullo, Richard M. Murray, Augusto Sarti  
 
| title = Control on the Sphere and Reduced Attitude Stabilization
 
| title = Control on the Sphere and Reduced Attitude Stabilization
| source = CDS Technical Report 95-005
+
| source = 1995 IFAC Symposium on Nonlinear Control Systems Design
| year = 1995
+
| year = 1994
| type = CDS Technical Report
+
| type = Converence paper
 
| funding =  
 
| funding =  
| url = ftp://ftp.cds.caltech.edu/pub/cds/techreports/postscript/cds95-005.pdf
+
| url = http://www.cds.caltech.edu/~murray/preprints/bms95-nolcos.pdf
 
| abstract =  
 
| abstract =  
This paper focuses on a new geometric approach to (fully actuated)
+
This paper focuses on a new geometric approach to fully actuated control
control systems on the sphere.  Our control laws exploit the basic and
+
systems on the Riemannian manifold S^2.  Our control laws exploit the basic
intuitive notions of geodesic direction and of distance between
+
and intuitive notions of geodesic direction and of distance between points,
points, and generalize the classical proportional plus derivative
+
and generalize the classical proportional plus derivative feedback (PD)
feedback (PD) without the need of arbitrary local coordinate charts.
+
without the need of arbitrary local coordinate charts. Even for the
The stability analysis relies on an appropriate Lyapunov function,
+
stability analysis, the appropriate Lyapunov function relies upon the notion
where the notion of distance and its properties are exploited.  This
+
of distance and its properties.  This methodology then applies to spin-axis
methodology then applies to spin-axis stabilization of a spacecraft
+
stabilization of a spacecraft actuated by only two control torques:
actuated by only two control torques: discarding the rotation about
+
discarding the rotation about the unactuated axis, a reduced system is
the unactuated axis, a reduced system is considered, whose state is in
+
considered, whose state is in fact defined on the sphere.  For this reduced
fact defined on the sphere.  For this reduced stabilization problem
+
attitude stabilization problem our approach allows us not only to deal
our approach allows us not only to deal optimally with the inevitable
+
optimally with the inevitable singularity, but also to achieve simplicity,
singularity, but also to achieve simplicity, versatility and
+
versatility and (coordinate independent) adaptive capabilities.
(coordinate independent) adaptive capabilities.
 
 
| flags = NoRequest
 
| flags = NoRequest
| tag = bm95a-cds
+
| tag = bms95-nolcos
| id = 1995q
+
| id = 1994i
 
}}
 
}}

Latest revision as of 06:20, 15 May 2016


Francesco Bullo, Richard M. Murray, Augusto Sarti
1995 IFAC Symposium on Nonlinear Control Systems Design

This paper focuses on a new geometric approach to fully actuated control systems on the Riemannian manifold S^2. Our control laws exploit the basic and intuitive notions of geodesic direction and of distance between points, and generalize the classical proportional plus derivative feedback (PD) without the need of arbitrary local coordinate charts. Even for the stability analysis, the appropriate Lyapunov function relies upon the notion of distance and its properties. This methodology then applies to spin-axis stabilization of a spacecraft actuated by only two control torques: discarding the rotation about the unactuated axis, a reduced system is considered, whose state is in fact defined on the sphere. For this reduced attitude stabilization problem our approach allows us not only to deal optimally with the inevitable singularity, but also to achieve simplicity, versatility and (coordinate independent) adaptive capabilities.