A Geometric Approach to Trajectory Design for an Autonomous Underwater Vehicle: Surveying the Bulbous Bow of a Ship

In this paper, we present a control strategy design technique for an autonomous underwater vehicle based on solutions to the motion planning problem derived from differential geometric methods. The motion planning problem is motivated by the practical application of surveying the hull of a ship for implications of harbor and port security. In recent years, engineers and researchers have been collaborating on automating ship hull inspections by employing autonomous vehicles. Despite the progresses made, human intervention is still necessary at this stage. To increase the functionality of these autonomous systems, we focus on developing model-based control strategies for the survey missions around challenging regions, such as the bulbous bow region of a ship. Recent advances in differential geometry have given rise to the field of geometric control theory. This has proven to be an effective framework for control strategy design for mechanical systems, and has recently been extended to applications for underwater vehicles. Advantages of geometric control theory include the exploitation of symmetries and nonlinearities inherent to the system. Here, we examine the posed inspection problem from a path planning viewpoint, applying recently developed techniques from the field of differential geometric control theory to design the control This research is supported in part by National Science Foundation grant DMS-0608583, and in part by Office of Naval Research grants N00014-03-1-0969, N00014-04-1-0751 and N00014-04-1-0751. R.N. Smith: Computer Science Department, Robotic Embedded Systems Laboratory, 3710 S. MClintock Avenue, Ronald Tutor Hall (RTH 512), University of Southern California, Los Angeles, CA 90089 M. Chyba: Mathematics Department, College of Natural Sciences, University of Hawai‘i, Honolulu, HI 96822, USA D. Cazzaro, L. Invernizzi: College of Engineering, Sant’Anna School of Advanced Studies, Pisa, Pi, 56127, Italy G. Marani, S.K. Choi: Autonomous Systems Laboratory, College of Engineering, University of Hawai‘i, Honolulu, HI 96822, USA February 18, 2010 DRAFT