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.