Related papers: Dynamical Systems in Elliptical Pursuit and Evasio…
We present a method for pursuit/evasion that is highly efficient and and scales to large teams of aircraft. The underlying algorithm is an efficient algorithm for solving Markov Decision Processes (MDPs) that supports fully continuous state…
This paper considers the problem of fast and safe autonomous navigation in partially known environments. Our main contribution is a control policy design based on ellipsoidal trajectory bounds obtained from a quadratic state-dependent…
Many dynamical systems exhibit similar structure, as often captured by hand-designed simplified models that can be used for analysis and control. We develop a method for learning to correspond pairs of dynamical systems via a learned latent…
A system of $N$ interacting objects with internal degrees of freedom is considered. Derivation of system of equations for the description of two interacting objects with spin is given. Relations between the parameters describing subsystems…
We investigate a minimal chase-and-escape model on a two-dimensional square lattice with randomly distributed static obstacles, focusing on how geometric disorder controls collective pursuit dynamics. Chasers and escapers move according to…
The aim of this work is to compare the orbital dynamics in three different models describing the properties of a star cluster rotating around its parent galaxy in a circular orbit. In particular, we use the isochrone and the Hernquist…
The dynamical friction experienced by a body moving in a gaseous medium is different from the friction in the case of a collisionless stellar system. Here we consider the orbital evolution of a gravitational perturber inside a gaseous…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
A fundamental challenge in learning an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. We formulate a mathematical definition of what it means to safely learn a dynamical system by…
In this paper, we present a game-theoretic feedback terminal guidance law for an autonomous, unpowered hypersonic pursuit vehicle that seeks to intercept an evading ground target whose motion is constrained in a one-dimensional space. We…
We consider the planar circular equilateral restricted four body-problem where a test particle of infinitesimal mass is moving under the gravitational attraction of three primary bodies which move on circular orbits around their common…
Given a chaotic dynamical system and a time interval in which some quantity takes an unusually large average value, what can we say of the trajectory that yields this deviation? As an example, we study the trajectories of the archetypical…
We present a framework that incorporates the idea of bounded rationality into dynamic stochastic pursuit-evasion games. The solution of a stochastic game is characterized, in general, by its (Nash) equilibria in feedback form. However,…
The trajectory and the orbital velocity are determined for an object moving in a gravitational system, in terms of fundamental and independent variables. In particular, considering a path on equipotential line, the elliptical orbit is…
Collision avoidance in the presence of dynamic obstacles in unknown environments is one of the most critical challenges for unmanned systems. In this paper, we present a method that identifies obstacles in terms of ellipsoids to estimate…
This paper studies a multiplayer reach-avoid differential game in the presence of general polygonal obstacles that block the players' motions. The pursuers cooperate to protect a convex region from the evaders who try to reach the region.…
Bifurcation equations, non-degeneracy and transversality conditions are obtained for the fold, transcritical, pitchfork and flip bifurcations for periodic points of one dimensional implicitly defined discrete dynamical systems. The backward…
In the last years, a growing number of challenging applications in navigation, logistics, and tourism were modeled as orienteering problems. This problem has been proposed in relation to a sport race where certain control points must be…
We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path…
Two-player pursuit-evasion differential game and time optimal zero control problem in $\ell^2$ are considered. Optimal control for the corresponding zero control problem is found. A strategy for the pursuer that guarantees the solution for…