Geometric Control Theory and its Application to Underwater Vehicles

(Department of Mathematics) The proposed research is based on theoretical study and experiments which extend geometric con-trol theory to practical applications within the field of marine science. In particular, we apply geometric methods to solve the motion planning problem for underwater vehicles. Bridging the gap between theory and application is the ultimate goal of control theory. Major developments have occurred recently in the field of geometric control which narrow this gap and which promote research linking theory and applica-tion. The work presented here is based on this recent progress with the objective to develop efficient tools for scientists and engineers in ocean research. On one hand, the underwater vehicle presents an ideal platform to extend known theory to mechanical systems which include dissipative and potential forces. And, on the other hand, the underwater vehicle application successfully demonstrates the applicability of geometric methods to design implementable motion planning solutions for concrete applications. 1 Goals, Objectives and Impact RESEARCH GOAL 1.1. It is a goal of this research to combine mathematics and ocean engineering through the application of differential geometry to the motion planning problem for underwater vehicles