Monograph records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 13:24:54 +0000Proportional Derivative (PD) Control on the Euclidean Group
https://resolver.caltech.edu/CaltechCDSTR:1995.CIT-CDS-95-010
Authors: {'items': [{'id': 'Bullo-F', 'name': {'family': 'Bullo', 'given': 'Francesco'}}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}]}
Year: 1995
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).https://authors.library.caltech.edu/records/wgq2y-5kk21Control on the Sphere and Reduced Attitude Stabilization
https://resolver.caltech.edu/CaltechCDSTR:1995.CIT-CDS-95-005
Authors: {'items': [{'id': 'Bullo-F', 'name': {'family': 'Bullo', 'given': 'Francesco'}}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}, {'id': 'Sarti-A', 'name': {'family': 'Sarti', 'given': 'Augusto'}}]}
Year: 1995
This paper focuses on a new geometric approach to (fully actuated)
control systems on the sphere. 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.
The stability analysis relies on an appropriate Lyapunov function,
where the notion of distance and its properties are exploited. 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 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.https://authors.library.caltech.edu/records/fjkqw-v1p46Tracking for Fully Actuated Mechanical Systems: A Geometric Framework
https://resolver.caltech.edu/CaltechCDSTR:1997.CIT-CDS-97-003
Authors: {'items': [{'id': 'Bullo-F', 'name': {'family': 'Bullo', 'given': 'Francesco'}}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}]}
Year: 1997
We present a general framework for the control of Lagrangian
systems with as many inputs as degrees of freedom. Relying on the geometry
of mechanical systems on manifolds, we propose a design algorithm for
the tracking problem. The notion of error function and transport map
lead to a proper definition of configuration and velocity error. These
are the crucial ingredients in designing a proportional derivative
feedback and feedforward controller. The proposed approach includes as
special cases a variety of results on control of manipulators, pointing
devices and autonomous vehicles. Our design provides particular insight
into both aerospace and underwater applications where the configuration
manifold is a Lie group.https://authors.library.caltech.edu/records/qh0me-t9d81