Steady Turns and Optimal Paths for Underwater Gliders

This paper describes analysis of steady turning motions for a new type of highly efficient underwater vehicle which uses gravity for propulsio n. Underwater gliders are winged underwater vehicles which locomote by modulating their buoyancy and their attitude. Several such vehicles have been developed and have already proven their worth as long-endurance ocean sampling platforms. The ultimate aim of our research is to develop optimal motion control strategies which further enhance the natural efficiency of these vehicles by minimizing the energy expended by the control system. First and foremost, the predominant vehicle motions should be stable, steady motions requiring little or no additional control effort. Moreover, these motions should be blended in a way that minimizes control effort. The primary contribution of this paper is an approximate analytical expression for steady turning motion obtained via regular perturbation analysis of a general and realistic vehicle model. The solution suggests a well-known time-optimal path planning procedure developed for a general type of nonholonomic mobile robot known as Dubins car. Assuming quasi-steady glider motions, time-optimality of Dubins paths corresponds to energy-optimality of underwater glider paths.