Related papers: Dynamical Systems in Elliptical Pursuit and Evasio…
Motion planning and control are two core components of the robotic systems autonomy stack. The standard approach to combine these methodologies comprises an offline/open-loop stage, planning, that designs a feasible and safe trajectory to…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…
The settling dynamics of spherical and elliptical particles in a viscous Newtonian fluid are investigated numerically using a finite difference technique. The terminal velocity for spherical particles is calculated for different system…
We study a finite-horizon differential game of pursuit-evasion like, between a single player and a mass of agents. The player and the mass directly control their own evolution, which for the mass is given by a first order PDE of transport…
Inspired by the classical Kepler and Rutherford problem, we investigate an analogous set-up in the context of active microswimmers: the behavior of a deformable microswimmer in a swirl flow. First we identify new steady bound states in the…
We investigate the dynamical systems modeling conflict processes between a pair of opponents. We assume that opponents are given on a common space by distributions (probability measures) having the similar or self-similar structure. Our…
In this paper, we investigate the quest for a single target, that remains fixed in a lattice, by a set of independent walkers. The target exhibits a fluctuating behavior between trap and ordinary site of the lattice, whereas the walkers…
Ground robots navigating in complex, dynamic environments must compute collision-free trajectories to avoid obstacles safely and efficiently. Nonconvex optimization is a popular method to compute a trajectory in real-time. However, these…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
Nonreciprocal interaction crowd systems, such as human-human, human-vehicle, and human-robot systems, often have serious impacts on pedestrian safety and social order. A more comprehensive understanding of these systems is needed to…
In this paper I consider the self-excited rotation of an elliptical cylinder towed in a viscous fluid as a canonical model of nonlinear fluid structure interactions with possible applications in the design of sensors and energy extraction…
Dynamical systems can autonomously adapt their organization so that the required target dynamics is reproduced. In the previous Rapid Communication [Phys. Rev. E 90,030901(R) (2014)], it was shown how such systems can be designed using…
The equations of motion of a secularly precessing ellipse are developed using time as the independent variable. The equations are useful when integrating numerically the perturbations about a reference trajectory which is subject to secular…
A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
Traditionally, the delay margin of a looped system is computed by considering both the controller and system representations that evolve in the same space (e.g. either continuous or discrete-time). However, as in practice the system is…
This paper analyzes the meeting time between a pair of pursuer and evader performing random walks on digraphs. The existing bounds on the meeting time usually work only for certain classes of walks and cannot be used to formulate…
Recently discrete dynamical models of walking droplet dynamics have allowed for fast numerical simulations of their horizontal chaotic motion and consequently the long-time statistical distribution of the droplet position. We develop a…
This paper addresses a critical aerial defense challenge in contested airspace, involving three autonomous aerial vehicles -- a hostile drone (the pursuer), a high-value drone (the evader), and a protective drone (the defender). We present…
Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and…