Detecting and Tracking Level Sets of Scalar Fields using a Robotic Sensor Network

We introduce an algorithm which detects and traces a specified level set of a scalar field (a contour) on a plane. A network of static sensor nodes with limited communication and processing are deployed in a planar environment along with a mobile node which can both sense and move. As the mobile node moves through the environment, it computes the local spatial gradient of the field by communicating with its immediate neighbors in the static sensor network. The algorithm causes the mobile node to perform gradient descent on the scalar field till it arrives at a location on the desired contour. From this point onwards, the algorithm drives the mobile node to trace the desired contour without departing from it. Experiments in simulation indicate that the required contour is found with reasonable accuracy (between 80-90%) for networks with node degree of greater than or equal to six. Our results also indicate that the paths generated by our algorithm are near-optimal in terms of the distance traversed by the mobile node. Our preliminary experimental results with a physical robot show that our algorithm is feasible.