Arian Panah to present this Friday

Everyone is cordially invited to hear Arian Panah present a talk on his MASc work: “Nonuniform Coverage with Time-Varying Risk Density Function”. The abstract of the talk is attached.  The talk will start promptly at 2:30pm.

Date: Friday February 27

Time: 2:30pm

Room: CBY D207


Multi-agent systems are extensively used in several civilian and military applications, such as surveillance, space exploration, cooperative classification, and search and rescue, to name a few. An important class of applications involves the optimal spatial distribution of a group of mobile robots on a given area, where the optimality refers to the assignment of subregions to the robots, in such a way that a suitable coverage metric is maximized. Typically the coverage metric encodes a risk distribution defined on the area, and a measure of the performance of individual robots with respect to points inside the region of interest. The risk density can be used to assign spatial distributions of risk in the region, as for example typically happens in surveillance applications in which high value units have to be protected against external threats coming into a given area surrounding them.

The solution of the optimal control problem in which the metric is autonomous (a function of time only through the state of the robots) is well known in the literature, with the optimal location of the robots given by the centroids of the Voronoi regions forming a Voronoi tessellation of the area. In other words, when the set of mobile robots configure themselves as the centroids of the Voronoi tessellation dictated by the coverage metric, the coverage itself is maximized.

In this work we advance on this result by considering a generalized area control problem in which the coverage metric is non-autonomous, that is the coverage metric is time varying independently of the states of the robots. This generalization is motivated by the study of coverage control problems in which the coordinated motion of a set of mobile robots accounts for the kinematics of objects penetrating from the outside. Asymptotic convergence and optimality of the non-autonmous system are studied by means of Barbalat’s Lemma, and connections with the kinematics of the moving intruders is established. Several numerical simulation results are used to illustrate theoretical predictions.

Amir Baradaran presented last Friday

Amir presented his MASc thesis work last Friday on “Development and Implementation of a Preconditioner for a Five-Moment One-Dimensional Moment Closure”. Supervisor Dr James McDonald was on hand for the presentation.

Traditionally, the Euler or Navier-Stokes equations are used to describe the time-evolution of a gas in the continuum regime. However, when a gas leaves the continuum regime and non-equilibrium effects become significant, neither of those two models produce physically accurate predictions.

Recently, a new system of first-order hyperbolic partial differential equations (PDEs) was proposed for the treatment of monatomic gases that is valid both in and for significant departures from local thermal equilibrium. In this study, the resulting system for a one-dimensional gas is studied. It consists of first-order hyperbolic PDEs. The numerical computation ofvthe system has proven to be difficult since, for some realistic states, the closing flux of the system becomes infinitely large. In the present study, the technique of preconditioning is used to develop a preconditioner for the system to scale the closing flux in order to remove the infinity from the system without altering the solution of the system in any way. A numerical implementation of the preconditioned system is described. Numerical solutions of several continuum and non-equilibrium flows problems are shown. Comparisons are made with other classical models.