Cooperative Gradient-Free Localization and Tracking of Moving Environmental Boundaries by Teams of Nonholonomic Robots

A team of Dubins-vehicle-like robots travels in a plane that hosts an unpredictably varying scalar field. The team has to find and then closely follow the moving and deforming level set (isoline) where the field assumes a pre-specified value, and also has to autonomously achieve an effective self-distribution along the isoline, with the even one being the ideal option. Any robot can measure only the field value at the current location and the relative positions of the peers within a finite range of sensing; an exchange of data within a finite communication range is possible. Every robot is controlled by its longitudinal acceleration and angular velocity, which are limited in absolute value; the longitudinal speeds are bounded from both above and below with given constants. We present a hybrid navigation law that solves the mission; in particular, it ensures an effective self-distribution of the team along the isoline, which comes to the even one if the isoline eventually stops. The proposed law does not rely on estimation of the field’s gradient. Mathematically rigorous justification of this law is provided and its effectiveness is confirmed by computer simulation tests.