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.

在本文中，我们考虑了可以由时变闭合曲线表示的环境边界。我们使用配备位置传感器的n个机器人对动态边界进行采样。预测过程中的主要困难在于，每个时间步长只能观察到n个边界点。我们的方法将有限傅里叶级数用于形状估计，并将多项式拟合用于时间点跟踪。这种组合提供了描述边界形状及其动力学的连续参数函数。我们在仿真和使用实际机器人进行的实验中验证了我们的策略。我们在非凸边界上进行了测试，假设测量值嘈杂且运动执行器不正确。