3 research outputs found
Coverage and Field Estimation on Bounded Domains by Diffusive Swarms
In this paper, we consider stochastic coverage of bounded domains by a
diffusing swarm of robots that take local measurements of an underlying scalar
field. We introduce three control methodologies with diffusion, advection, and
reaction as independent control inputs. We analyze the diffusion-based control
strategy using standard operator semigroup-theoretic arguments. We show that
the diffusion coefficient can be chosen to be dependent only on the robots'
local measurements to ensure that the swarm density converges to a function
proportional to the scalar field. The boundedness of the domain precludes the
need to impose assumptions on decaying properties of the scalar field at
infinity. Moreover, exponential convergence of the swarm density to the
equilibrium follows from properties of the spectrum of the semigroup generator.
In addition, we use the proposed coverage method to construct a
time-inhomogenous diffusion process and apply the observability of the heat
equation to reconstruct the scalar field over the entire domain from
observations of the robots' random motion over a small subset of the domain. We
verify our results through simulations of the coverage scenario on a 2D domain
and the field estimation scenario on a 1D domain.Comment: To appear in the proceedings of the 55th IEEE Conference on Decision
and Control (CDC 2016