Stability analysis of swarms

Gazi, Veysel; Passino, K.M.

doi:10.1109/acc.2002.1023830

Cited by 202 publications

(210 citation statements)

References 27 publications

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“…In [2] and [3], we considered a biologically inspired n-dimensional continuous-time synchronous swarm model based on artificial potentials, and obtained results on cohesive swarm aggregation. In [4], the model in [2] and [3] was augmented with a term representing the environment, and convergence to (divergence from) more favorable regions (unfavorable regions) was shown. Similar results based on artificial potentials and virtual leaders were independently obtained by Leonard et al in [5] and [6] for agents with point-mass dynamics.…”

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confidence: 99%

Swarm aggregations using artificial potentials and sliding-mode control

2005

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In this paper, we consider a control strategy of multiagent systems, or simply, swarms, based on artificial potential functions and the sliding-mode control technique. First, we briefly discuss a "kinematic" swarm model in -dimensional space introduced in an earlier paper. In that model, the interindividual interactions are based on artificial potential functions, and the motion of the individuals is along the negative gradient of the combined potential. After that, we consider a general model for vehicle dynamics of each agent (swarm member), and use sliding-mode control theory to force their motion to obey the dynamics of the kinematic model. In this context, the results for the initial model serve as a "proof of concept" for multiagent coordination and control (swarm aggregation), whereas the present results serve as a possible implementation method for engineering swarms with given vehicle dynamics. The presented control scheme is robust with respect to disturbances and system uncertainties.

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confidence: 99%

Swarm aggregations using artificial potentials and sliding-mode control

2005

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“…A consensus algorithm is an interaction rule that governs the information exchange between a dynamic agent and all of its neighbors in the network. Notwithstanding original studies in the area of computer science (particularly in distributed computation and automata), the consensus problems discussed previously have been studied extensively in the context of distributed coordination of dynamic networks, partly due to the potential applications including congestion control in communication networks, cooperative control of multiple vehicle systems, formation control, swarming and flocking, distributed sensor network, attitude alignment of groups of satellites, air traffic control, and many others [17–20]. …”

Section: Introductionmentioning

confidence: 99%

Stability Switches of Arbitrary High‐Order Consensus in Multiagent Networks with Time Delays

Yang

2013

The Scientific World Journal

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High-order consensus seeking, in which individual high-order dynamic agents share a consistent view of the objectives and the world in a distributed manner, finds its potential broad applications in the field of cooperative control. This paper presents stability switches analysis of arbitrary high-order consensus in multiagent networks with time delays. By employing a frequency domain method, we explicitly derive analytical equations that clarify a rigorous connection between the stability of general high-order consensus and the system parameters such as the network topology, communication time-delays, and feedback gains. Particularly, our results provide a general and a fairly precise notion of how increasing communication time-delay causes the stability switches of consensus. Furthermore, under communication constraints, the stability and robustness problems of consensus algorithms up to third order are discussed in details to illustrate our central results. Numerical examples and simulation results for fourth-order consensus are provided to demonstrate the effectiveness of our theoretical results.

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“…With the increasing intensity of external noise, the system undergoes a remarkable transition from an ordered state to a disordered state . In recent years, the Vicsek model has drawn more and more attention from the physics, biology, engineering and social science communities [2], [3], [19], [21]–[27]. As two representative following works, Jadbabaie et al .…”

Section: Introductionmentioning

confidence: 99%

“…Apart from the motion synchronization investigation, other scholars turned to study more deeply into the nature of aggregation patterns [19], [28]–[33]. Enlightened by the mechanism of the inter-molecule force, Breder [28] proposed a simplified attraction/repulsion (A/R) model composed of a constant attraction term and a repulsion term inversely proportional to the square of the inter-agent distance, whereas Warburton and Lazarus [29] studied the effects on cohesion of a family of A/R functions.…”

Section: Introductionmentioning

confidence: 99%

“…Enlightened by the mechanism of the inter-molecule force, Breder [28] proposed a simplified attraction/repulsion (A/R) model composed of a constant attraction term and a repulsion term inversely proportional to the square of the inter-agent distance, whereas Warburton and Lazarus [29] studied the effects on cohesion of a family of A/R functions. More recently, Gazi and Passino [19] derived another A/R model which is closer to the inter-molecule force function, and analytically proved that a stable ring-shaped pattern can be yielded in a finite time. Analogously, by using a linearized A/R model, Moreau [24] proved that the group will form a bounded circularly moving pattern if and only if there exists an agent connecting to all other ones, directly or indirectly, over an arbitrary time interval.…”

Section: Introductionmentioning

confidence: 99%

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Aggregation Pattern Transitions by Slightly Varying the Attractive/Repulsive Function

et al. 2011

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Among collective behaviors of biological swarms and flocks, the attractive/repulsive (A/R) functional links between particles play an important role. By slightly changing the cutoff distance of the A/R function, a drastic transition between two distinct aggregation patterns is observed. More precisely, a large cutoff distance yields a liquid-like aggregation pattern where the particle density decreases monotonously from the inside to the outwards within each aggregated cluster. Conversely, a small cutoff distance produces a crystal-like aggregation pattern where the distance between each pair of neighboring particles remains constant. Significantly, there is an obvious spinodal in the variance curve of the inter-particle distances along the increasing cutoff distances, implying a legible transition pattern between the liquid-like and crystal-like aggregations. This work bridges the aggregation phenomena of physical particles and swarming of organisms in nature upon revealing some common mechanism behind them by slightly varying their inter-individual attractive/repulsive functions, and may find its potential engineering applications, for example, in the formation design of multi-robot systems and unmanned aerial vehicles (UAVs).

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Stability analysis of swarms

Cited by 202 publications

References 27 publications

Swarm aggregations using artificial potentials and sliding-mode control

Swarm aggregations using artificial potentials and sliding-mode control

Stability Switches of Arbitrary High‐Order Consensus in Multiagent Networks with Time Delays

Aggregation Pattern Transitions by Slightly Varying the Attractive/Repulsive Function

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