Abstract: A method for dealing with the problem of convergence to incorrect equilibrium points of distance-based formation controllers was recently proposed by introducing an additional controlled variable, ...

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Topics: Control variable (53%), Convergence (routing) (53%), Equilibrium point (53%)

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9 results found

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Farhad Mehdifar^{1}, Charalampos P. Bechlioulis^{2}, Farzad Hashemzadeh^{3}, Mahdi Baradarannia^{3}•Institutions (3)

Abstract: This paper presents a novel control protocol for robust distance-based formation control with prescribed performance in which agents are subjected to unknown external disturbances Connectivity maintenance and collision avoidance among neighboring agents are also handled by the appropriate design of certain performance bounds that constrain the inter-agent distance errors As an extension to the proposed scheme, distance-based formation centroid maneuvering is also studied for disturbance-free agents, in which the formation centroid tracks a desired time-varying velocity The proposed control laws are decentralized, in the sense that each agent employs local relative information regarding its neighbors to calculate its control signal Therefore, the control scheme is implementable on the agents’ local coordinate frames Using rigid graph theory, input-to-state stability, and Lyapunov based analysis, the results are established for minimally and infinitesimally rigid formations in 2-D or 3-D space Furthermore, it is argued that the proposed approach increases formation robustness against shape distortions and can prevent formation convergence to incorrect shapes under the effect of external disturbances, which is likely to happen in conventional distance-based formation control methods Finally, extensive simulation studies clarify and verify the proposed approach

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Topics: Lyapunov function (52%), Robustness (computer science) (51%), Multi-agent system (51%) ... show more

19 Citations

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Farhad Mehdifar^{1}, Charalampos P. Bechlioulis^{2}, Farzad Hashemzadeh^{3}, Mahdi Baradarannia^{3}•Institutions (3)

17 Nov 2019-

Abstract: This paper presents a novel control protocol for robust distance-based formation control with prescribed performance in which agents are subjected to unknown external disturbances. Connectivity maintenance and collision avoidance among neighboring agents are also handled by the appropriate design of certain performance bounds that constrain the inter-agent distance errors. As an extension to the proposed scheme, distance-based formation centroid maneuvering is also studied for disturbance-free agents, in which the formation centroid tracks a desired time-varying velocity. The proposed control laws are decentralized, in the sense that each agent employs local relative information regarding its neighbors to calculate its control signal. Therefore, the control scheme is implementable on the agents' local coordinate frames. Using rigid graph theory, input-to-state stability, and Lyapunov based analysis, the results are established for minimally and infinitesimally rigid formations in 2-D or 3-D space. Furthermore, it is argued that the proposed approach increases formation robustness against shape distortions and can prevent formation convergence to incorrect shapes, which is likely to happen in conventional distance-based formation control methods. Finally, extensive simulation studies clarify and verify the proposed approach.

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Topics: Lyapunov function (52%), Robustness (computer science) (52%), Multi-agent system (51%) ... show more

8 Citations

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Abstract: A well known problem with distance-based formation control is the existence of multiple equilibrium points not associated with the desired formation. This problem can be mitigated by introducing an additional controlled variable. In this paper, we consider distance + area (or angle) schemes for 2D formations of single-integrator agents. By using directed graphs and triangulation of the n -agent formation, we introduce switching control laws that ensure the asymptotic stability of the desired formation for almost all initial agent positions. The state-dependent switching strategy is designed to force the formation to escape the subspaces of the incorrect equilibria. The switching strategy also allows us to remove restrictions on the shape of the desired formation that were present in previous results.

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5 Citations

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30 Dec 2019-

Abstract: In this paper, we develop a hybrid distance-angle rigidity theory that involves heterogeneous distances (or unsigned angles) and signed constraints for a framework in the 2-D and 3-D space. The new rigidity theory determines a (locally) unique formation shape up to a translation and a rotation by a set of distance and signed constraints, or up to a translation, a rotation and additionally a scaling factor by a set of unsigned angle and signed constraints. Under this new rigidity theory, we have a clue to resolve the flip (or reflection) and flex ambiguity for a target formation with hybrid distance-angle constraints. In particular, we can completely eliminate the ambiguity issues if formations are under a specific construction which is called \myemph{signed Henneberg construction} in this paper. We then apply the rigidity theory to formation shape control and develop a gradient-based control system that guarantees an exponential convergence close to a desired formation by inter-neighbor measurements. Several numerical simulations on formation shape control with hybrid distance-angle constraints are provided to validate the theoretical results.

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Topics: Rotation (mathematics) (50%)

4 Citations

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01 Aug 2020-

Abstract: In this paper, we propose a novel approach to the problem of augmenting distance-based formation controllers with a secondary feedback variable for the purpose of preventing formation ambiguities. We introduce two variables that form an orthogonal space and uniquely characterize a triangular formation in two dimensions. We show that the resulting controller ensures the almost-global asymptotic stability of the desired formation for an $n$ -agent system without conditions on the triangulations of the desired formation or control gains.

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Topics: Control theory (52%), Control system (51%)

3 Citations

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28 results found

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Abstract: In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.

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Topics: Consensus dynamics (65%), Uniform consensus (61%), Network topology (57%) ... show more

10,379 Citations

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Abstract: There has been a shift from the general presumption that “doctor knows best” to a heightened respect for patient autonomy. Medical ethics remains one-sided, however. It tends (incorrectly) to interpret patient autonomy as mere participation in decisions, rather than a willingness to take the consequences. In this respect, medical ethics remains largely paternalistic, requiring doctors to protect patients from the consequences of their decisions. This is reflected in a one-sided account of duties in medical ethics. Medical ethics may exempt patients from obligations because they are the weaker or more vulnerable party in the doctor-patient relationship. We argue that vulnerability does not exclude obligation. We also look at others ways in which patients’ responsibilities flow from general ethics: for instance, from responsibilities to others and to the self, from duties of citizens, and from the responsibilities of those who solicit advice. Finally, we argue that certain duties of patients counterbalance an otherwise unfair captivity of doctors as helpers.

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Topics: Nursing ethics (83%), Medical ethics (65%)

9,859 Citations

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01 Jan 2008-

Abstract: The coordinated use of autonomous vehicles has an abundance of potential applications from the domestic to the hazardously toxic. Frequently the communications necessary for the productive interplay of such vehicles may be subject to limitations in range, bandwidth, noise and other causes of unreliability. Information consensus guarantees that vehicles sharing information over a network topology have a consistent view of information critical to the coordination task. Assuming only neighbor-neighbor interaction between vehicles, Distributed Consensus in Multi-vehicle Cooperative Control develops distributed consensus strategies designed to ensure that the information states of all vehicles in a network converge to a common value. This approach strengthens the team, minimizing power consumption and the deleterious effects of range and other restrictions. The monograph is divided into six parts covering introductory, theoretical and experimental material and featuring: an overview of the use of consensus algorithms in cooperative control; consensus algorithms in single- and double-integrator dynamical systems; consensus algorithms for rigid-body attitude dynamics; rendezvous and axial alignment, formation control, deep-space formation flying, fire monitoring and surveillance. Notation drawn from graph and matrix theory and background material on linear and nonlinear system theory are enumerated in six appendices. The authors maintain a website at which can be found a sample simulation and experimental video material associated with experiments in several chapters of this book. Academic control systems researchers and their counterparts in government laboratories and robotics- and aerospace-related industries will find the ideas presented in Distributed Consensus in Multi-vehicle Cooperative Control of great interest. This text will also serve as a valuable support and reference for graduate courses in robotics, and linear and nonlinear control systems.

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Topics: Consensus (59%)

2,413 Citations

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Sergio Garrido-Jurado^{1}, Rafael Muñoz-Salinas^{1}, F. J. Madrid-Cuevas^{1}, Manuel J. Marín-Jiménez^{1}•Institutions (1)

Abstract: This paper presents a fiducial marker system specially appropriated for camera pose estimation in applications such as augmented reality and robot localization. Three main contributions are presented. First, we propose an algorithm for generating configurable marker dictionaries (in size and number of bits) following a criterion to maximize the inter-marker distance and the number of bit transitions. In the process, we derive the maximum theoretical inter-marker distance that dictionaries of square binary markers can have. Second, a method for automatically detecting the markers and correcting possible errors is proposed. Third, a solution to the occlusion problem in augmented reality applications is shown. To that aim, multiple markers are combined with an occlusion mask calculated by color segmentation. The experiments conducted show that our proposal obtains dictionaries with higher inter-marker distances and lower false negative rates than state-of-the-art systems, and provides an effective solution to the occlusion problem. HighlightsWe propose an algorithm for generating configurable marker dictionaries.We derive the maximum theoretical inter-marker distance.A method for automatically detecting the markers and correcting errors is proposed.A solution to the occlusion problem in augmented reality applications is shown.

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Topics: Augmented reality (54%), Fiducial marker (53%), Pose (51%)

1,210 Citations

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26 Dec 1995-

Abstract: Numbers and Elementary Mathematics Proofs without words Constants Special numbers Number theory Series and products Algebra Elementary algebra Polynomials Vector algebra Linear and matrix algebra Abstract algebra Discrete Mathematics Set theory Combinatorics Graphs Combinatorial design theory Difference equations Geometry Euclidean geometry Coordinate systems in the plane Plane symmetries or isometries Other transformations of the plane Lines Polygons Surfaces of revolution: the torus Quadrics Spherical geometry and trigonometry Conics Special plane curves Coordinate systems in space Space symmetries or isometries Other transformations of space Direction angles and direction cosines Planes Lines in space Polyhedra Cylinders Cones Differential geometry Analysis Differential calculus Differential forms Integration Table of indefinite integrals Table of definite integrals Ordinary differential equations Partial differential equations Integral equations Tensor analysis Orthogonal coordinate systems Interval analysis Real analysis Generalized functions Complex analysis Special Functions Ceiling and floor functions Exponentiation Logarithmic functions Exponential function Trigonometric functions Circular functions and planar triangles Tables of trigonometric functions Angle conversion Inverse circular functions Hyperbolic functions Inverse hyperbolic functions Gudermannian function Orthogonal polynomials Gamma function Beta function Error functions Fresnel integrals Sine, cosine, and exponential integrals Polylogarithms Hypergeometric functions Legendre functions Bessel functions Elliptic integrals Jacobian elliptic functions Clebsch-Gordan coefficients Integral transforms: Preliminaries Fourier integral transform Discrete Fourier transform (DFT) Fast Fourier transform (FFT) Multidimensional Fourier transforms Laplace transform Hankel transform Hartley transform Mellin transform Hilbert transform Z-Transform Tables of transforms Probability and Statistics Probability theory Classical probability problems Probability distributions Queuing theory Markov chains Random number generation Control charts and reliability Statistics Confidence intervals Tests of hypotheses Linear regression Analysis of variance (ANOVA) Sample size Contingency tables Probability tables Scientific Computing Basic numerical analysis Numerical linear algebra Numerical integration and differentiation Mathematical Formulae from the Sciences Acoustics Astrophysics Atmospheric physics Atomic physics Basic mechanics Beam dynamics Classical mechanics Coordinate systems - Astronomical Coordinate systems - Terrestrial Earthquake engineering Electromagnetic transmission Electrostatics and magnetism Electronic circuits Epidemiology Finance Fluid mechanics Fuzzy logic Human body Image processing matrices Macroeconomics Modeling physical systems Optics Population genetics Quantum mechanics Quaternions Relativistic mechanics Solid mechanics Statistical mechanics Thermodynamics Miscellaneous Calendar computations Cellular automata Communication theory Control theory Computer languages Cryptography Discrete dynamical systems and chaos Electronic resources Elliptic curves Financial formulae Game theory Knot theory Lattices Moments of inertia Music Operations research Recreational mathematics Risk analysis and decision rules Signal processing Symbolic logic Units Voting power Greek alphabet Braille code Morse code List of References List of Figures List of Notation Index

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Topics: Special functions (67%), Generalized function (65%), Vector space (65%) ... show more

654 Citations