Estimating boundary dynamics using robotic sensor networks with pointwise measurements

Abstract

In this paper, we consider environmental boundaries that can be represented by a time-varying closed curve. We use n robots equipped with location sensors to sample the dynamic boundary. The main difficulty during the prediction process is that only n boundary points can be observed at each time step. Our approach combines finite Fourier series for shape-estimation and polynomial fitting for point tracking in time. This combination gives a continuous parametric function that describes the boundary shape and its dynamics. We validate our strategy in simulation and with experiments using actual robots. We tested on non-convex boundaries assuming noisy measurements and inaccurate motion actuators.

Fourier-Based Multi-Agent Formation Control to Track Evolving Closed Boundaries

“…The algorithm in [24] uses the advection-diffusion equation to model the dynamics of plumes and to control a team of robots that monitor them. The method in [25] describes a solution to estimate time-varying boundaries with multiple robots. Note that most existing methods in the literature mainly focus on detecting/estimating the boundaries, and do not exploit the properties of parametric curves in their design.…”

Fourier-Based Multi-Agent Formation Control to Track Evolving Closed Boundaries

“…The algorithm in [24] uses the advection-diffusion equation to model the dynamics of plumes and to control a team of robots that monitor them. The method in [25] describes a solution to estimate time-varying boundaries with multiple robots. Note that most existing methods in the literature mainly focus on detecting/estimating the boundaries, and do not exploit the properties of parametric curves in their design.…”