861 research outputs found
Zeros of Networked Systems with Time-invariant Interconnections
This paper studies zeros of networked linear systems with time-invariant
interconnection topology. While the characterization of zeros is given for both
heterogeneous and homogeneous networks, homogeneous networks are explored in
greater detail. In the current paper, for homogeneous networks with
time-invariant interconnection dynamics, it is illustrated how the zeros of
each individual agent's system description and zeros definable from the
interconnection dynamics contribute to generating zeros of the whole network.
We also demonstrate how zeros of networked systems and those of their
associated blocked versions are related.Comment: Preprint submitted for possible publication in Automatic
Simultaneous Velocity and Position Estimation via Distance-only Measurements with Application to Multi-Agent System Control
This paper proposes a strategy to estimate the velocity and position of
neighbor agents using distance measurements only. Since with agents executing
arbitrary motions, instantaneous distance-only measurements cannot provide
enough information for our objectives, we postulate that agents engage in a
combination of circular motion and linear motion. The proposed estimator can be
used to develop control algorithms where only distance measurements are
available to each agent. As an example, we show how this estimation method can
be used to control the formation shape and velocity of the agents in a multi
agent system. Simulation results are provided to illustrate the performance of
the proposed algorithm.Comment: Submitted to IEEE Transactions on Automatic Control as a Technical
Not
3D Mobile Localization Using Distance-only Measurements
For a group of cooperating UAVs, localizing each other is often a key task.
This paper studies the localization problem for a group of UAVs flying in 3D
space with very limited information, i.e., when noisy distance measurements are
the only type of inter-agent sensing that is available, and when only one UAV
knows a global coordinate basis, the others being GPS-denied. Initially for a
two-agent problem, but easily generalized to some multi-agent problems,
constraints are established on the minimum number of required distance
measurements required to achieve the localization. The paper also proposes an
algorithm based on semidefinite programming (SDP), followed by maximum
likelihood estimation using a gradient descent initialized from the SDP
calculation. The efficacy of the algorithm is verified with experimental noisy
flight data.Comment: Submitted to IEEE Transactions on Aerospace and Electronic System
Distributed estimation and control for preserving formation rigidity for mobile robot teams
Inspired by the concept of network algebraic connectivity, we adopt an
extended notion named rigidity preservation index to characterize the rigidity
property for a formation framework. A gradient based controller is proposed to
ensure the rigidity preservation of multi-robot networks in an unknown
environment, while the rigidity metric can be maximized over time during
robots' motions. In order to implement the controller in a distributed manner,
a distributed inverse power iteration algorithm is developed which allows each
robot to estimate the global rigidity index information. Simulation results are
provided to demonstrate the effectiveness of the estimation and control scheme.Comment: 8 pages, 3 figure
Network Flows that Solve Linear Equations
We study distributed network flows as solvers in continuous time for the
linear algebraic equation . Each node has
access to a row of the matrix and the
corresponding entry in the vector . The first "consensus +
projection" flow under investigation consists of two terms, one from standard
consensus dynamics and the other contributing to projection onto each affine
subspace specified by the and . The second "projection
consensus" flow on the other hand simply replaces the relative state feedback
in consensus dynamics with projected relative state feedback. Without
dwell-time assumption on switching graphs as well as without positively lower
bounded assumption on arc weights, we prove that all node states converge to a
common solution of the linear algebraic equation, if there is any. The
convergence is global for the "consensus + projection" flow while local for the
"projection consensus" flow in the sense that the initial values must lie on
the affine subspaces. If the linear equation has no exact solutions, we show
that the node states can converge to a ball around the least squares solution
whose radius can be made arbitrarily small through selecting a sufficiently
large gain for the "consensus + projection" flow under fixed bidirectional
graphs. Semi-global convergence to approximate least squares solutions is
demonstrated for general switching directed graphs under suitable conditions.
It is also shown that the "projection consensus" flow drives the average of the
node states to the least squares solution with complete graph. Numerical
examples are provided as illustrations of the established results.Comment: IEEE Transactions on Automatic Control, in pres
A Double-Layered Framework for Distributed Coordination in Solving Linear Equations
This paper proposes a double-layered framework (or form of network) to
integrate two mechanisms, termed consensus and conservation, achieving
distributed solution of a linear equation. The multi-agent framework considered
in the paper is composed of clusters (which serve as a form of aggregating
agent) and each cluster consists of a sub-network of agents. By achieving
consensus and conservation through agent-agent communications in the same
cluster and cluster-cluster communications, distributed algorithms are devised
for agents to cooperatively achieve a solution to the overall linear equation.
These algorithms outperform existing consensus-based algorithms, including but
not limited to the following aspects: first, each agent does not have to know
as much as a complete row or column of the overall equation; second, each agent
only needs to control as few as two scalar states when the number of clusters
and the number of agents are sufficiently large; third, the dimensions of
agents' states in the proposed algorithms do not have to be the same (while in
contrast, algorithms based on the idea of standard consensus inherently require
all agents' states to be of the same dimension). Both analytical proof and
simulation results are provided to validate exponential convergence of the
proposed distributed algorithms in solving linear equations
Network Flows that Solve Least Squares for Linear Equations
This paper presents a first-order {distributed continuous-time algorithm} for
computing the least-squares solution to a linear equation over networks. Given
the uniqueness of the solution, with nonintegrable and diminishing step size,
convergence results are provided for fixed graphs. The exact rate of
convergence is also established for various types of step size choices falling
into that category. For the case where non-unique solutions exist, convergence
to one such solution is proved for constantly connected switching graphs with
square integrable step size, and for uniformly jointly connected switching
graphs under the boundedness assumption on system states. Validation of the
results and illustration of the impact of step size on the convergence speed
are made using a few numerical examples
Circumnavigation Using Distance Measurements (Extended Version)
Consider a stationary agent A at an unknown location and a mobile agent
B that must move to the vicinity of and then circumnavigate A at a prescribed
distance from A. In doing so, B can only measure its distance from A, and knows
its own position in some reference frame. This paper considers this problem,
which has applications to surveillance or maintaining an orbit. In many of
these applications it is difficult for B to directly sense the location of A,
e.g. when all that B can sense is the intensity of a signal emitted by A. This
intensity does, however provide a measure of the distance. We propose a
nonlinear periodic continuous time control law that achieves the objective.
Fundamentally, B must exploit its motion to estimate the location of A, and use
its best instantaneous estimate of where A resides, to move itself to achieve
the ultimate circumnavigation objective. The control law we propose marries
these dual goals and is globally exponentially convergent. We show through
simulations that it also permits B to approximately achieve this objective when
A experiences slow, persistent and potentially nontrivial drift.Comment: 6 pages, The extended version of the paper in Proc. European Control
Conference 200
Higher order mobile coverage control with application to localization
Most current results on coverage control using mobile sensors require that
one partitioned cell is associated with precisely one sensor. In this paper, we
consider a class of coverage control problems involving higher order Voronoi
partitions, motivated by applications where more than one sensor is required to
monitor and cover one cell. Such applications are frequent in scenarios
requiring the sensors to localize targets. We introduce a framework depending
on a coverage performance function incorporating higher order Voronoi cells and
then design a gradient-based controller which allows the multi-sensor system to
achieve a local equilibrium in a distributed manner. The convergence properties
are studied and related to Lloyd algorithm. We study also the extension to
coverage of a discrete set of points. In addition, we provide a number of real
world scenarios where our framework can be applied. Simulation results are also
provided to show the controller performance.Comment: submitted to Automatica. arXiv admin note: text overlap with
arXiv:1410.194
Finite-Time Distributed Linear Equation Solver for Minimum Norm Solutions
This paper proposes distributed algorithms for multi-agent networks to
achieve a solution in finite time to a linear equation where has
full row rank, and with the minimum -norm in the underdetermined case
(where has more columns than rows). The underlying network is assumed to be
undirected and fixed, and an analytical proof is provided for the proposed
algorithm to drive all agents' individual states to converge to a common value,
viz a solution of , which is the minimum -norm solution in the
underdetermined case. Numerical simulations are also provided as validation of
the proposed algorithms
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