All are cordially invited to a graduate seminar talk to be given by Mostafa Fallah. He will give talk titled “Coordinated Deployment of Multiple Autonomous Agents in Area Coverage Problems with Evolving Risk.”
Date: Friday March 20th
Room: CBY D207
Coordinated missions with platoons of autonomous agents are rapidly becoming popular because of technological advances in computing, networking, miniaturization and combination of electromechanical systems. These multi-agents networks coordinate their actions to perform challenging spatially-distributed tasks such as search, survey, exploration, and mapping. Environmental monitoring and locational optimization are among the main applications of the emerging technology of wireless sensor networks where the optimality refers to the assignment of sub-regions to each agent, in such a way that a suitable coverage metric is maximized. Usually the coverage metric encodes a distribution of risk 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 quantify spatial distributions of risk in the domain.
The solution of the optimal control problem in which the risk measures are not time varying is well known in the literature, with the optimal configuration of the robots given by the centroids of the Voronoi regions forming a centroidal Voronoi tessellation of the area. In other words, when the set of mobile robots converge to the corresponding centroids of the Voronoi tessellation dictated by the coverage metric, the coverage itself is maximized.
In this work, we consider a time-varying risk density function evolving according to a diffusion equation with varying boundary conditions that quantify a time-varying risk on the border of the workspace. Boundary conditions model a time varying flux of external threats coming into the area, averaged over the boundary length, so that we do not consider the individual kinematics of incoming threats but rather their averaged, distributed effect. This approach is similar to the one commonly adopted in continuum physics, in which kinematic descriptors are averaged over spatial domain and suitable continuum fields are introduced to describe their evolution. By adopting a first gradient constitutive relation between the flux and the density, we obtain a simple diffusion equation. Asymptotic convergenceand optimality of the non-autonomous system are studied by means of Barbalat’s Lemma and connections with varying boundary conditions are established. Some criteria on time-varying boundary conditions and its evolution are established to guarantee the stabilities of agents’ trajectories. A set of numerical simulations illustrate the theoretical results.