The Artistic Geometry of Consensus Protocols

Tsiotras, Panagiotis; Castro, Luis I. Reyes

doi:10.1007/978-3-319-03904-6_6

Cited by 22 publications

(7 citation statements)

References 30 publications

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“…Future research can include unicycle models or quadrotor models to be closer to reality. Moreover, this type of dynamic gains control can be applied to similar MAS with structurally unstable networks, e.g., to systems in [18].…”

Section: Discussionmentioning

confidence: 99%

“…As a remark, the form A(θ i (t)) can be applied to any system with fixed gains. In [18], authors show that their network is also depicting epicycle and trochoid, and this formation relies on the eigenvalues of A. Moreover, if the Laplacian is taken such that L = circ.…”

Section: Performance Very Good Good Excellentmentioning

confidence: 99%

“…It leads the overall network to have purely imaginary axis eigenvalues. The requirement of possessing imaginary-axis eigenvalues is also the backbone of Tsiotras' paper where it was shown that a marginally stable system is a magnificent and simple way to generate artistic patterns [18]. Juang carried out the analysis and added a new rigidity gain, leading also to a multiple imaginary-axis eigenvalues configuration, which renders a class of epicycle patterns.…”

Section: Introductionmentioning

confidence: 99%

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Robust Formation Maintenance Methods under General Topology Pursuit of Multi-Agents Systems

2021

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In this article, methods of formation maintenance for a group of autonomous agents under ageneral topology scheme are discussed. Unlike rendezvous or geometric formation, general topology pursuit allows the group of agents to autonomously form trochoid patterns, which are useful in civilian and military applications. However, this type of topology is established by designing a marginally stable system that may be sensitive to parameter variations. To account for this drawback of stability, linear fixed-gains are turned into a dynamical version in this paper. By implementing a disturbance observer controller, systems are shown to maintain their formation despite the disturbances or uncertainties. Comparison in the effectiveness of the presented method with model reference adaptive control and integral sliding mode control under the uncertainties of the gains is also conducted. The capabilities of controllers are demonstrated and supported through simulations.

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Section: Discussionmentioning

confidence: 99%

Section: Performance Very Good Good Excellentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust Formation Maintenance Methods under General Topology Pursuit of Multi-Agents Systems

2021

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“…By employing a single agent, a plethora of patterns were achieved by Sinha A., Tripathy T. et al throughout various approaches and algorithms [15][16][17][18][19]. By deploying more agents under a general cyclic scheme, it was possible to generate epicycle or trochoidal-like patterns for a groups of agents modeled as single integrator [20][21][22][23]; which is of interest in the present paper. In these papers, the control law developed to reach epicycle or trochoidal patterns uses fixed-gain methods.…”

Section: Introductionmentioning

confidence: 94%

Integral Sliding Control Approach for Generalized Cyclic Pursuit Formation Maintenance

Ansart

Juang

2021

Electronics

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This paper is concerned with the formation maintenance of a group of autonomous agents under generalized cyclic pursuit (GCP) law. The described pattern for agents under such formation is epicycle-like. For a network of agents to achieve such a formation, marginal stability of the overall network is required. The desired marginal stability of the network relies on each agents’ gain values, and uncertainties in these gains can occur. Previous studies have used fixed gains, we enhance the stability of the gains via a dynamic approach using an integral sliding controller (ISC). An ISC can ensure sliding behavior of the gains throughout the entire response, and it is shown that the gains are robust toward variations and thus make the network keep its marginal stability and its formation.

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“…Indeed, trochoidal curves are the natural wind-dependent extension of Dubins-type paths and have been studied in the literature as a solution to a boundary value problem to connect two states in the presence of wind [24]. In [25], and in the preliminary work [26], it is shown how elaborate patterns that are closely related to hypocycloid and epicycloid curves can be generated as the paths followed by a team of interacting agents moving on the plane. The agents considered are of the single integrator type and the generation of hypocycloid and epicycloid depends on a suitable gain matrix and the choice of an appropriate connectivity graph between the agents.…”

Section: Introductionmentioning

confidence: 99%

Emergent Hypotrochoidal and Epitrochoidal Formations in a Swarm of Agents

Fedele

D’Alfonso

Bono

2023

IEEE Trans. Automat. Contr.

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This paper proposes a decentralised controller for a swarm of agents that generates hypotrochoidal and epitrochoidal curves in 3D space. The dynamics of the agents is modelled as a double integrator where the control input, i.e. the acceleration profile, contains two terms that account for the interactions between the agents in terms of position and velocity, respectively. The term related to the interaction between velocities is weighted by a skew-symmetric matrix responsible for coupling the velocities displacements. Such a matrix defines an axis of rotation centred on the centroid of the swarm, around which the swarm organises itself to generate the desired trajectories, which can be selected by properly setting two free parameters of the model. In particular, the motion of each agent is analysed by separating its dynamics along the rotation axis from that in the perpendicular plane. It is shown that the agents achieve consensus or periodic motion along the axis of rotation while performing the desired evolutions in the perpendicular plane. Numerical simulations are presented to illustrate the proposed framework.

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The Artistic Geometry of Consensus Protocols

Cited by 22 publications

References 30 publications

Robust Formation Maintenance Methods under General Topology Pursuit of Multi-Agents Systems

Robust Formation Maintenance Methods under General Topology Pursuit of Multi-Agents Systems

Integral Sliding Control Approach for Generalized Cyclic Pursuit Formation Maintenance

Emergent Hypotrochoidal and Epitrochoidal Formations in a Swarm of Agents

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