Section: New Results

Marine Robotic Surveys

Participants : Frédéric Mazenc, Michael Malisoff [Louisiana State University] , Fumin Zhang [Georgia Tech.] .

The works [24] , [61] was inspired by the recent Deepwater Horizon oil spill disaster. The goal was to develop and implement robotic surveying methods to evaluate the immediate and longer term environmental impacts of the oil spills. It was joint with Michael Malisoff from the LSU and a Georgia Tech robotics team led by Fumin Zhang. Robotic surveying methods provide a low cost and convenient way to collect data in marsh areas that are difficult to access by human based methods. We designed strict Lyapunov functions that made it possible to use ISS to quantify the robustness of collision avoiding curve tracking controllers under controller uncertainty. The controllers are designed to keep the robot a fixed distance from, but moving parallel to, a two dimensional curve. Four challenges in applying ISS to curve tracking are (a) the need to restrict the magnitudes of the uncertainty to keep the state in the state space and build a strict Lyapunov function, (b) the likelihood of time delays in the controllers in real time applications, (c) possible parameter uncertainty such as unknown control gains, and (d) generalizations to three dimensional curve tracking. We overcame challenge (a) by finding maximum bounds on the perturbations that maintain forward invariance of a nested family of hexagons that fill the state space and transforming a nonstrict Lyapunov function into a strict Lyapunov function on the full state space. To address challenge (b), we used a Lyapunov-Krasovskii approach from [119] to convert the strict Lyapunov function into a Lyapunov-Krasovskii functional. This led to an upper bound on the admissible controller delay that can be introduced into the controller while still maintaining ISS.