Related papers: Natural frames and interacting particles in three …
This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the…
Let a finite set of interacting particles be given, together with a symmetry Lie group $G$. Here we describe all possible dynamics that are jointly equivariant with respect to the action of $G$. This is relevant e.g., when one aims to…
This paper presents a three dimensional collision avoidance approach for aerial vehicles inspired by coordinated behaviors in biological groups. The proposed strategy aims to enable a group of vehicles to converge to a common destination…
In this paper, we study the emergence of circular formation for agents in cyclic pursuit. Each agent is a unicycle traveling at a fixed common forward speed. We first establish a necessary and sufficient condition for the existence of…
A fundamental control problem for autonomous vehicle formations is formation shape control, in which the agents must maintain a prescribed formation shape using only information measured or communicated from neighboring agents. While a…
We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group $D_{3d}$. Group theory greatly facilitates the application…
We classify the interactions between self-propelled particles moving at a constant speed from symmetry considerations. We establish a systematic expansion for the two-body forces in the spirit of a multipolar expansion. This formulation…
The problem of 3-dimensional, convex rigid-body collision over a plane is fully investigated; this includes bodies with sharp corners that is resolved without the need for nonsmooth convex analysis of tangent and normal cones. In…
We investigate a one-dimensional system of $N$ particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the $N$ particles do…
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…
Formation control deals with the design of decentralized control laws that stabilize mobile, autonomous agents at prescribed distances from each other. We call any configuration of the agents a target configuration if it satisfies the…
We consider the problem of steering a collection of n particles that obey identical n-dimensional linear dynamics via a common state feedback law towards a rearrangement of their positions, cast as a controllability problem for a dynamical…
Relational particle models are of value in the absolute versus relative motion debate. They are also analogous to the dynamical formulation of general relativity, and as such are useful for investigating conceptual strategies proposed for…
With the aim of understanding the emergence of collective motion from local interactions of organisms in a "noisy" environment, we study biologically inspired, inherently non-equilibrium models consisting of self-propelled particles. In…
In the formation control problem for autonomous robots a distributed control law steers the robots to the desired target formation. A local stability result of the target formation can be derived by methods of linearization and center…
The most general 2+1 dimensional spinning particle model is considered. The action functional may involve all the possible first order Poincare invariants of world lines, and the particular class of actions is specified thus the…
We discuss biologically inspired, inherently non-equilibrium self-propelled particle models, in which the particles interact with their neighbours by choosing at each time step the local average direction of motion. We summarize some of the…
This paper deals with the modeling and mathematical analysis of vehicular traffic phenomena according to a kinetic theory approach, where the microscopic state of vehicles is described by: (i) position, (ii) velocity, as a continuous…
The Gipps car-following model is a widely used tool for studying and simulation traffic dynamics. Despite its popularity an often disregarded property is that under heterogeneous parametrization on the individual vehicles in the traffic…
Directly interacting particles are considered in the multitime formalism of predictive relativistic mechanics. When the equations of motion leave a phase-space volume invariant, it turns out that the phase average of any first integral,…