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Multiple people tracking is a key problem for many applications such as surveillance, animation or car navigation, and a key input for tasks such as activity recognition. In crowded environments occlusions and false detections are common,…

Collaborative signal processing and sensor deployment have been among the most important research tasks in target tracking using networked sensors. In this paper, the mathematical model is formulated for single target tracking using mobile…

The optimal cooperative guidance in the nonlinear setting for intercepting a target by multiple pursuers is studied in the paper. As certain relative angles can improve observability, the guidance command is required to cooperatively…

Tracking on the rotation group is a key component of many modern systems for estimation of the motion of rigid bodies. To address this problem, here we describe a Bayesian algorithm that relies on directional measurements for tracking on…

We rigorously show that a class of systems of partial differential equations modeling wave bifurcations supports stationary equivariant bifurcation dynamics through deriving its full dynamics on the center manifold(s). A direct consequence…

In order to describe the velocity and the anaerobic energy of two runners competing against each other for middle-distance races, we present a mathematical model relying on an optimal control problem for a system of ordinary differential…

Predicting the motion of dynamic agents is a critical task for guaranteeing the safety of autonomous systems. A particular challenge is that motion prediction algorithms should obey dynamics constraints and quantify prediction uncertainty…

This paper investigates the stochastic moving target encirclement problem in a realistic setting. In contrast to typical assumptions in related works, the target in our work is non-cooperative and capable of escaping the circle containment…

This article deals with the modeling for an individual car path through a road network, where the dynamics is driven by a coupled system of ordinary and partial differential equations. The network is characterized by bounded buffers at…

This paper presents a model-based, adaptive, nonlinear controller for the bicopter stabilization and trajectory-tracking problem. The nonlinear controller is designed using the backstepping technique. Due to the non-invertibility of the…

We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following…

We introduce a dynamic vehicle routing problem in which a single vehicle seeks to guard a circular perimeter against radially inward moving targets. Targets are generated uniformly as per a Poisson process in time with a fixed arrival rate…

This paper presents a new mathematical model of vehicular traffic, based on the methods of the generalized kinetic theory, in which the space of microscopic states (position and velocity) of the vehicles is genuinely discrete. While in the…

We analyze predator-prey dynamics in one dimension in which a Brownian predator adopts a chasing strategy that consists in stochastically resetting its current position to locations previously visited by a diffusive prey. We study three…

A general and psychologically plausible collision avoidance driver model can improve transportation safety significantly. Most computational driver models found in the literature have used control theory methods only, and they are not…

Due to the inherent safety concerns associated with traffic movement in unconstrained two-dimensional settings, it is important that pedestrians' and other modes' movements such as bicyclists are modeled as a risk-taking stochastic dynamic…

We study a spatial predator-prey model in which prey can enter a protection zone (refuge) inaccessible to predators, while predators exhibit directed movement toward prey-rich regions. The directed movement is modeled by a far-sighted…

This paper examines the optimal velocity follow-the-leader dynamics, a microscopic traffic model, and explores different aspects of the dynamical model, with particular emphasis on collision analysis. More precisely, we present a rigorous…

Consider the dynamics of two point masses on a surface of constant curvature subject to an attractive force analogue of Newton's inverse square law. When the distance between the bodies is sufficiently small, the reduced equations of motion…

The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…