Martin Rosalie

Systematic template extraction from chaotic attractors: I. Genus-one attractors with an inversion symmetry

Describing the topological properties by a template is a powerful technique to classify chaotic attractors. Most of the time, reduced templates are used, but direct templates—in which all mechanisms (torsions, branch permutation, etc) identified in the attractor are explicitly described without any simplification—are of great interest for a better description of the subtleties of the dynamics. We introduce here two additional conventions for representing in a unique way the reduced template from a given linking matrix. We then propose an addition law for linking matrices which allows us to manipulate (combine) different mechanisms. A direct template can thus be described by using a series of linking matrices. On 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.

Systematic template extraction from chaotic attractors: II. Genus-one attractors with multiple unimodal folding mechanisms

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 Poincare section. Resulting from a merging attractor crisis, these attractors can be easily described as being made of two folding 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 the description of 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 Poincare 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 Poincare section.

A cancer model for the angiogenic switch

The occurrence of metastasis is an important feature in cancer development. In order to have a one-site model taking into account the interactions between host, effector immune and tumor cells which is not only valid for the early stages of tumor growth, we developed in this paper a new model where are incorporated interactions of these three cell populations with endothelial cells. These latter cells are responsible for the neo-vascularization of the tumor site which allows the migration of tumor cells to distant sites. It is then shown that, for some parameter values, the resulting model for the four cell populations reproduces the angiogenic switch, that is, the transition from avascular to vascular tumor.

Templates and subtemplates of Rössler attractors from a bifurcation diagram

We study the bifurcation diagram of the Rossler 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 detail how the templates of these attractors are subtemplates of a unique template. Our main result is that only one template describes the topological structure of eight 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.

Using heterogeneous multilevel swarms of UAVs and high-level data fusion to support situation management in surveillance scenarios

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.

Toward a General Procedure for Extracting Templates from Chaotic Attractors Bounded by High Genus Torus

The topological analysis of chaotic attractor by means of template is rather well established for simple attractors as solution to the Rossler 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 Poincare 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 Poincare section and whose bounding torus has g interior holes aligned. An example with g = 5 — a multispiral attractor — is explicitly treated.

From Random Process to Chaotic Behavior in Swarms of UAVs

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 UAV trajectories that still ensures a high area coverage.

UAV Multilevel Swarms for Situation Management

The development and usage of Unmanned Aerial Vehicles (UAVs) quickly increased in the last decades, mainly for military purposes. Nowadays, this type of technology is used in non-military contexts mainly for civil and environment protection: search & rescue teams, fire fighters, police officers, environmental scientific studies, etc. Although the technology for operating a single UAV is now mature, additional efforts are still necessary for using UAVs in fleets (or swarms). This position paper presents the ASIMUT project (Aid to SItuation Management based on MUltimodal, MUltiUAVs, MUltilevel acquisition Techniques). The challenges of this project consist of handling several fleets of UAVs (swarms) including communication, networking and positioning aspects. This motivates the development of novel multilevel cooperation algorithms which is an area that has not been widely explored, especially when autonomy is an additional challenge. Moreover, we will provide techniques to optimize communications for multilevel swarms. Finally, we will develop distributed and localized mobility management algorithms that will cope with conflicting objectives such as connectivity maintenance and geographical area coverage.

Area exploration with a swarm of UAVs combining deterministic chaotic ant colony mobility with position MPC

The recent advances in Unmanned Aerial Vehicles (UAVs) technology permit to develop new usages for them. One of the current challenges is to operate UAVs as an autonomous swarm. In this domain we already proposed a new mobility model using Ant Colony Algorithms combined with chaotic dynamics (CACOC) to enhance the coverage of an area by a swarm of UAVs. In this paper we propose to consider this mobility model as waypoints for real UAVs. A control model of the UAVs is deployed to test the efficiency of the coverage of an area by the swarm. We have tested our approach in a realistic robotics simulator (V-Rep) which is connected with ROS. We compare the performance in terms of coverage using several metrics to ensure that this mobility model is efficient for real UAVs.

Collision Avoidance Effects on the Mobility of a UAV Swarm Using Chaotic Ant Colony with Model Predictive Control

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.