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For motion planning and control of autonomous vehicles to be proactive and safe, pedestrians' and other road users' motions must be considered. In this paper, we present a vehicle motion planning and control framework, based on Model…
This article introduces a representation of dynamic meshes, adapted to some numerical simulations that require controlling the volume of objects with free boundaries, such as incompressible fluid simulation, some astrophysical simulations…
We present in this paper a very adapted finite volume numerical scheme for transport type-equation. The scheme is an hybrid one combining an anti-dissipative method with down-winding approach for the flux and an high accurate method as the…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Employing physically-consistent numerical methods is an important step towards attaining robust and accurate numerical simulations. When addressing compressible flows, in addition to preserving kinetic energy at a discrete level, as done in…
We propose a new finite volume scheme for the Euler system of gas dynamics motivated by the model proposed by H. Brenner. Numerical viscosity imposed through upwinding acts on the velocity field rather than on the convected quantities. The…
This extensive review was written for the ``Encyclopedia of Complexity and System Science'' (Springer, 2008) and addresses a broad audience ranging from engineers to applied mathematicians, computer scientists and physicists. It provides an…
In this paper, we introduce and study one-dimensional models for the behavior of pedestrians in a narrow street or corridor. We begin at the microscopic level by formulating a stochastic cellular automata model with explicit rules for…
This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real world problems is…
In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We…
In this paper we study a two dimensional crowd model where pedestrian velocity consists of two elements: a non--local interaction term, modeling the effect of other walkers on each individual, and a control term. This latter term can be…
In this paper we devise a microscopic (agent-based) mathematical model for reproducing crowd behaviour in a specific scenario: a number of pedestrians, consisting of numerous social groups, flow along a corridor until a gate located at the…
This contribution proposes a method to make agents in a microscopic simulation of pedestrian traffic walk approximately along a path of estimated minimal remaining travel time to their destination. Usually models of pedestrian dynamics are…
While the use of technology to provide accurate and objective measurements of human movement performance is presently an area of great interest, efforts to quantify the performance of movement are hampered by the lack of a principled model…
We propose a hierarchy of kinetic and macroscopic models for a system consisting of a large number of interacting pedestrians. The basic interaction rules are derived from earlier work where the dangerousness level of an interaction with…
This paper considers the problem of steering a vast group of agents of which the dynamics are governed by a discrete-time first-order linear system. The group of agents are characterized as a probability density function and an occupation…
Motion planning in uncertain environments like complex urban areas is a key challenge for autonomous vehicles (AVs). The aim of our research is to investigate how AVs can navigate crowded, unpredictable scenarios with multiple pedestrians…
Most traffic flow control algorithms address switching cycle adaptation of traffic signals and lights. This work addresses traffic flow optimisation by self-organising micro-level control combining Reinforcement Learning and rule-based…
This paper is devoted to the study of the dynamic optimization of several controlled crowd motion models in the general planar settings, which is an application of a class of optimal control problems involving a general nonconvex sweeping…
Port-Hamiltonian systems (PHS) theory is a recent but already well-established modelling approach for non-linear physical systems. Some studies have shown lately that PHS frameworks are relevant for modelling and control of swarm and…