1,746 research outputs found
Synchronization with partial state coupling on SO(n)
This paper studies autonomous synchronization of k agents whose states evolve
on SO(n), but which are only coupled through the action of their states on one
"reference vector" in Rn for each link. Thus each link conveys only partial
state information at each time, and to reach synchronization agents must
combine this information over time or throughout the network. A natural
gradient coupling law for synchronization is proposed. Extensive convergence
analysis of the coupled agents is provided, both for fixed and time-varying
reference vectors. The case of SO(3) with fixed reference vectors is discussed
in more detail. For comparison, we also treat the equivalent setting in Rn,
i.e. with states in Rn and connected agents comparing scalar product of their
states with a reference vector.Comment: to be submitted to SIAM Journal on Control and Optimizatio
Consensus on Nonlinear Spaces
peer reviewedConsensus problems have attracted significant attention in the control community
over the last decade. They act as a rich source of new mathematical problems pertaining to
the growing field of cooperative and distributed control. This paper is an introduction to
consensus problems whose underlying state-space is not a linear space, but instead a highly
symmetric nonlinear space such as the circle and other relevant generalizations. A geometric
approach is shown to highlight the connection between several fundamental models of consensus,
synchronization, and coordination, to raise significant global convergence issues not present in
linear models, and to be relevant for a number of engineering applications, including the design
of planar or spatial coordinated motions
Positioning and Scheduling of Wireless Sensor Networks - Models, Complexity, and Scalable Algorithms
Consensus and formation control on SE(3) for switching topologies
This paper addresses the consensus problem and the formation problem on
in multi-agent systems with directed and switching interconnection topologies. Several control laws are introduced for the consensus problem. By a simple transformation, it is shown that the proposed control laws can be used for the formation problem. The design is first conducted on the kinematic level, where the velocities are the control laws. Then, for rigid bodies in space, the design is conducted on the dynamic level, where the torques and the forces are the control laws. On the kinematic level, first two control laws are introduced that explicitly use Euclidean transformations, then separate control laws are defined for the rotations and the translations. In the special case of purely rotational motion, the consensus problem is referred to as consensus on
or attitude synchronization. In this problem, for a broad class of local representations or parameterizations of
, including the Axis–Angle Representation, the Rodrigues Parameters and the Modified Rodrigues Parameters, two types of control laws are presented that look structurally the same for any choice of local representation. For these two control laws we provide conditions on the initial rotations and the connectivity of the graph such that the system reaches consensus on
. Among the contributions of this paper, there are conditions for when exponential rate of convergence occurs. A theorem is provided showing that for any choice of local representation for the rotations, there is a change of coordinates such that the transformed system has a well known structure
Decentralized Adaptive Control for Collaborative Manipulation of Rigid Bodies
In this work, we consider a group of robots working together to manipulate a
rigid object to track a desired trajectory in . The robots do not know
the mass or friction properties of the object, or where they are attached to
the object. They can, however, access a common state measurement, either from
one robot broadcasting its measurements to the team, or by all robots
communicating and averaging their state measurements to estimate the state of
their centroid. To solve this problem, we propose a decentralized adaptive
control scheme wherein each agent maintains and adapts its own estimate of the
object parameters in order to track a reference trajectory. We present an
analysis of the controller's behavior, and show that all closed-loop signals
remain bounded, and that the system trajectory will almost always (except for
initial conditions on a set of measure zero) converge to the desired
trajectory. We study the proposed controller's performance using numerical
simulations of a manipulation task in 3D, as well as hardware experiments which
demonstrate our algorithm on a planar manipulation task. These studies, taken
together, demonstrate the effectiveness of the proposed controller even in the
presence of numerous unmodeled effects, such as discretization errors and
complex frictional interactions
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