Optimal Control of an Undersea Glider in a Symmetric Pull-up

Abstract

An undersea glider is a winged autonomous undersea vehicle which modulates its buoyancy to rise or sink and moves its center of mass to control pitch and roll attitude. By properly phasing buoyancy and pitch control, an undersea glider rectifies the vertical motion caused by changes in buoyancy into forward motion caused by the lift force on the fixed wing. The characteristic "porpoising" motion is useful in oceanographic surveys and the propulsion method is extremely efficient - undersea gliders routinely operate for months without human intervention. Glider efficiency could be improved even further by addressing the phenomenon of "stall" (loss of lift) when a glider transitions from downward to upward flight. Because the stall phenomenon occurs asymmetrically over the vehicle's wing, it can cause directional errors which must be corrected at a corresponding energetic cost. This paper describes the formulation of a point mass model and its dynamic equations of motion. An optimal control formulation was designed using angle of attack and buoyancy as controls to investigate control scheduling methods for avoiding stall in a symmetric pull-up. The calculations were repeated using three different numerical solution techniques for comparison of the methodologies and results. The model was updated to include longitudinal rigid body dynamics and changed the control to the rate of change of the longitudinal center of gravity location. This model allowed for the inclusion of added mass effects due to fluid displacement.