Describing the topological properties by a template is a powerful technique to classify chaotic attractors. Most of the time, reduced template are used but direct templates-in which all mechanisms (torsions, branch permutation, etc.) identified in the attractor are explicitely described without any simplification-are of a great interest to have a better description of the subtleties of the dynamics. We here introduce two additional conventions to represent in an unique way the reduced template from a given linking matrix. Then, we propose an addition law for linking matrices which allows to manipulate (combine) different mechanisms. Direct template can thus be described by using a series of linking matrices. In the other hand, we show how to analytically build the linking matrix associated with an attractor which is the image under an inversion symmetry of an attractor whose linking matrix is known.

The number of civilian and military applications using Unmanned Aerial Vehicles (UAVs) has increased during the last years and the forecasts for upcoming years are exponential. One of the current major challenges consist in considering UAVs as autonomous swarms to address some limitations of single UAV usage such as autonomy, range of operation and resilience. In this article we propose novel mobility models for multi-level swarms of collaborating UAVs used for the coverage of a given area. These mobility models generate unpredictable trajectories using a chaotic solution of a dynamical system. We detail how the chaotic properties are used to structure the exploration of an unknown area and enhance the exploration part of an Ant Colony Optimization method. Empirical evidence of the improvement of the coverage efficiency obtained by our mobility models is provided via simulation. It clearly outperforms state-of-the-art approaches.

We study the bifurcation diagram of the Rössler system. It displays the various dynamical regimes of the system (stable or chaotic) when a parameter is varied. We choose a diagram that exhibits coexisting attractors and banded chaos. We use the topological characterization method to study these attractors. Then, we details how the templates of these attractors are subtemplates of a unique template. Our main result is that only one template describe the topological structure of height attractors. This leads to a topological partition of the bifurcation diagram that gives the symbolic dynamic of all bifurcation diagram attractors with a unique template.

Unmanned Aerial Vehicles (UAVs) applications have seen an important increase in the last decade for both military and civilian applications ranging from fire and high seas rescue to military surveillance and target detection. While this technology is now mature for a single UAV, new methods are needed to operate UAVs in swarms, also referred to as fleets. This work focuses on the mobility management of one single autonomous swarm of UAVs which mission is to cover a given area in order to collect information. Several constraints are applied to the swarm to solve this problem due to the military context. First, the UAVs mobility must be as unpredictable as possible to prevent any UAV tracking. However the Ground Control Station (GCS) operator(s) still needs to be able to forecast the UAVs paths. Finally, the UAVs are autonomous in order to guarantee the mission continuity in a hostile environment and the method must be distributed to ensure fault-tolerance of the system. To solve this problem, we introduce the Chaotic Ant Colony Optimization to Coverage (CACOC) algorithm that combines an Ant Colony Optimization approach (ACO) with a chaotic dynamical system. CACOC permits to obtain a deterministic but unpredictable system. Its performance is compared to other state-of-the art models from the literature using several coverage-related metrics, i.e. coverage rate, recent coverage and fairness. Numerical results obtained by simulation underline the performance of our CACOC method: a deterministic method with unpredictable le UAV trajectories that still ensures a high area coverage.

Asymmetric and symmetric chaotic attractors produced by the simplest jerk equivariant system are topologically characterized. In the case of this system with an inversion symmetry, it is shown that symmetric attractors bounded by genus-one tori are conveniently analyzed using a two-components Poincaré section. Resulting from a merging attractor crisis, these attractors can be easily described as made of two foldings mechanisms (here described as mixers), one for each of the two attractors co-existing before the crisis: symmetric attractors are thus described by a template made of two mixers. We thus developed a procedure for concatenating two mixers (here associated with unimodal maps) into a single one, allowing to describe a reduced template, that is, a template simplified under an isotopy. The so-obtained reduced template is associated with a description of symmetric attractors based on one-component Poincaré section as suggested by the corresponding genus-one bounding torus. It is shown that several reduced templates can be obtained depending on the choice of the retained one-component Poincaré section.PACS numbers: 05.45.-a

The recent development of compact and economic small Unmanned Aerial Vehicles (UAVs) permits the development of new UAV swarm applications. In order to enhance the area coverage of such UAV swarms, a novel mobility model has been presented in previous work, combining an Ant Colony algorithm with chaotic dynamics (CACOC). This work is extending CACOC by a Collision Avoidance (CA) mechanism and testing its efficiency in terms of area coverage by the UAV swarm. For this purpose, CACOC is used to compute UAV target waypoints which are tracked by model predictively controlled UAVs. The UAVs are represented by realistic motion models within the virtual robot experimentation platform (V-Rep). This environment is used to evaluate the performance of the proposed CACOC with CA algorithm in an area exploration scenario with 3 UAVs. Finally, its performance is analyzed using metrics.

The development and usage of Unmanned Aerial Vehicles (UAVs) quickly increased in the last decades, mainly for military purposes. This technology is also now of high interest in non-military contexts like logistics, environmental studies and different areas of civil protection. While the technology for operating a single UAV is rather mature, additional efforts are still necessary for using UAVs in fleets (or swarms). The Aid to SItuation Management based on MUltimodal, MUltiUAVs, MUltilevel acquisition Techniques (ASIMUT) project which is supported by the European Defence Agency (EDA) aims at investigating and demonstrating dedicated surveillance services based on fleets of UAVs. The aim is to enhance the situation awareness of an operator and to decrease his workload by providing support for the detection of threats based on multi-sensor multi-source data fusion. The operator is also supported by the combination of information delivered by the heterogeneous swarms of UAVs and by additional information extracted from intelligence databases. As a result, a distributed surveillance system increasing detection, high-level data fusion capabilities and UAV autonomy is proposed

The topological analysis of chaotic attractor by means of template is rather well established for simple attractors as solution to the Rössler system. Lorenz-like attractors are already slightly more complicated because they are bounded by a genus-3 bounding torus, implying the necessity to use a two-component Poincaré section. In this paper, we enriched the concept of linking matrix to correctly describe an algebraic template for an attractor with (g - 1) components of Poincaré section and whose bounding torus has g interior holes aligned. An example with g = 5 — a multispiral attractor — is explicitly treated.