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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:03:54 +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.eduhttps://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.eduhttps://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.eduhttps://authors.library.caltech.edu/records/qh0me-t9d81Adaptive and Distributed Algorithms for Vehicle Routing in a Stochastic and Dynamic Environment
https://resolver.caltech.edu/CaltechAUTHORS:20111122-095750180
Authors: {'items': [{'id': 'Pavone-M', 'name': {'family': 'Pavone', 'given': 'Marco'}}, {'id': 'Frazzoli-E', 'name': {'family': 'Frazzoli', 'given': 'Emilio'}}, {'id': 'Bullo-F', 'name': {'family': 'Bullo', 'given': 'Francesco'}}]}
Year: 2011
DOI: 10.1109/TAC.2010.2092850
In this paper, we present adaptive and distributed algorithms for motion coordination of a group of m vehicles. The vehicles must service demands whose time of arrival, spatial location, and service requirement are stochastic; the objective is to minimize the average time demands spend in the system. The general problem is known as the m-vehicle Dynamic Traveling Repairman Problem (m-DTRP). The best previously known control algorithms rely on centralized task assignment and are not robust against changes in the environment. In this paper, we first devise new control policies for the 1-DTRP that: i) are provably optimal both in light-load conditions (i.e., when the arrival rate for the demands is small) and in heavy-load conditions (i.e., when the arrival rate for the demands is large), and ii) are adaptive, in particular, they are robust against changes in load conditions. Then, we show that specific partitioning policies, whereby the environment is partitioned among the vehicles and each vehicle follows a certain set of rules within its own region, are optimal in heavy-load conditions. Building upon the previous results, we finally design control policies for the m-DTRP that i) are adaptive and distributed, and ii) have strong performance guarantees in heavy-load conditions and stabilize the system in any load condition.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/725rm-mks35Distributed Algorithms for Environment Partitioning in Mobile Robotic Networks
https://resolver.caltech.edu/CaltechAUTHORS:20120124-111427134
Authors: {'items': [{'id': 'Pavone-M', 'name': {'family': 'Pavone', 'given': 'Marco'}}, {'id': 'Arsie-A', 'name': {'family': 'Arsie', 'given': 'Alessandro'}}, {'id': 'Frazzoli-E', 'name': {'family': 'Frazzoli', 'given': 'Emilio'}}, {'id': 'Bullo-F', 'name': {'family': 'Bullo', 'given': 'Francesco'}}]}
Year: 2011
DOI: 10.1109/TAC.2011.2112410
A widely applied strategy for workload sharing is to
equalize the workload assigned to each resource. In mobile multiagent systems, this principle directly leads to equitable partitioning policies whereby: 1) the environment is equitably divided into subregions of equal measure; 2) one agent is assigned to each subregion; and 3) each agent is responsible for service requests originating within its own subregion. The current lack of distributed algorithms for the computation of equitable partitions limits the
applicability of equitable partitioning policies to limited-size multiagent systems operating in known, static environments. In this paper, first we design provably correct and spatially distributed algorithms that allow a team of agents to compute a convex and equitable partition of a convex environment. Second, we discuss how these algorithms can be extended so that a team of agents can compute, in a spatially distributed fashion, convex and equitable partitions with additional features, e.g., equitable and median Voronoi diagrams. Finally, we discuss two application domains for our algorithms, namely dynamic vehicle routing for mobile robotic networks and wireless ad hoc networks. Through these examples, we show how one can couple the algorithms presented in this paper with equitable partitioning policies to make these amenable to distributed implementation. More in general, we illustrate a systematic approach to devise spatially distributed control policies for a large variety of multiagent coordination problems. Our approach is related to the classic Lloyd algorithm and exploits the unique features of power diagrams.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yn226-9nz10