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Abstract In this work, we investigate the analysis of generators for dynamic graphs, which are defined as graphs whose topology changes over time. We focus on generated graphs whose order (number of nodes) varies over time. We use a concept called “sustainability” to qualify the long-term evolution of dynamic graphs. A dynamic graph is considered sustainable if its evolution does not result in a static, empty, or periodic graph. To illustrate how the analysis can be conducted, a parameterized and probability-based generator, named D3G3 (Degree-Driven Dynamic Geometric Graphs Generator), has been introduced in a recent work. From this model, we derive multiple scenarios that correspond to three trends in graph order evolution. Our central contribution lies in a mathematical framework that provides an expectation of the order of the graph at time step $$t+1$$ t + 1 , given its order at time step t. Nevertheless, our analysis underscores the challenge of characterizing the sustainability of dynamic graphs, even when a formal mathematical model for graph order evolution is known.

This work concerns the autonomous navigation of non-holonomic ground mobile robots in a GPS-denied environment. The objective was to locate, in a global frame, without GPS, anonymous ground mobile robots starting from two consecutive aerial images captured by a single fixed webcam. The effectiveness of deep learning by a MultiLayer Perceptron in an indexed localization was compared to the methods studied in previous works. The ability of a robot to determine the position of other non-indexed robots was also performed. The structure and parameters of the network and the choice of the points taken into account during the learning phase to obtain a local optimum are presented. The results, obtained from simulated and experimental data, are compared to those obtained with more classical methods for different sampling periods (time between images).

Motivated by feedback from firefighters in Normandy, this work aims to provide a simple technique for a set of identical drones to collectively describe an arbitrary planar virtual shape in a 3D space in a decentralized manner. The original problem involved surrounding a toxic cloud to monitor its composition and short-term evolution. In the present work, the pattern is described using Fourier descriptors, a convenient mathematical formulation for that purpose. Starting from a reference point, which can be the center of a fire, Fourier descriptors allow for more precise description of a shape as the number of harmonics increases. This pattern needs to be evenly occupied by the fleet of drones under consideration. To optimize the overall view, the drones must be evenly distributed angularly along the shape. The proposed method enables virtual planar shape description, decentralized bearing angle assignment, drone movement from takeoff positions to locations along the shape, and collision avoidance. Furthermore, the method allows for the number of drones to change during the mission. The method has been tested both in simulation, through emulation, and in outdoor experiments with real drones. The obtained results demonstrate that the method is applicable in real-world contexts.

In a round-trip carsharing system, stations must be located in such a way that allow for maximum user coverage with the least walking distance as well as offer certain degrees of flexibility for returning. Therefore, a balance must be stricken between these factors. Providing a satisfactory system can be translated into an optimization problem and belongs to an NP-hard class. In this article, a novel optimization model for the round-trip carsharing fleet placement problem, called Fleet Placement Problem (FPP), is proposed. The optimization in this work is multiobjective and its NP-hard nature is proven. Three different optimization algorithms: PolySCIP (exact method), heuristics, and NSGA-II (metaheuristic) are investigated. This work adopts three real instances for the study, instead of their abstracts where they are most commonly used. They are two instance:, in the city of Luxembourg (smaller and larger) and a much larger instance in the city of Munich. Results from each algorithm are validated and compared with solution from human experts. Superiority of the proposed FPP model over the traditional methods is also demonstrated.