Non-Gradient Based Tracking of Environmental Field Isolines in a Changing Medium by Dubins-Vehicle Type Robots

A non-holonomic robot of a Dubins-vehicle type moves in a changing resistant medium, like water or air. The objective is to exhibit the extension of a spatial phenomenon (e.g., a critically contaminated area) related to a dynamic environmental field (e.g., a distribution of the contaminant concentration). Specifically, the robot should arrive at a certain level set of the field and repeatedly sweep it afterwards. The field data comes exclusively from online and point-wise measurements of the field value at the current location of the robot. An additional problem is related to the significant uncertainty on the field and the medium, including their variation with time and the effect of the medium on the robot's motion. The conditions for the accomplishability of the mission objective are found under these uncertainties and constraints on the kinematics of the robot. A navigation algorithm is presented that solves the mission with a slight enhancement of these necessary conditions. The performance of the algorithm is rigorously justified by the non-local convergence result and validated by computer simulation tests with a 6-DOF catamaran-like vessel and real-world environmental data.