Approximate Analytical Turning Conditions for Underwater Gliders: Implications for Motion Control and Path Planning

This paper describes analysis of steady motions for underwater gliders, a type of highly efficient underwater vehicle which uses gravity for propulsion. Underwater gliders are winged underwater vehicles which locomote by modulating their buoyancy and their attitude. Several underwater gliders have been developed and have proven their worth as efficient long-distance, long-duration ocean sampling platforms. Underwater gliders are so efficient because they spend much of their flight time in stable, steady motion. Wings-level gliding flight for underwater gliders has been well studied, but analysis of steady turning flight is more subtle. This paper presents an approximate analytical expression for steady turning motion for a realistic underwater glider model. The problem is formulated in terms of regular perturbation theory, with the vehicle turn rate as the perturbation parameter. The resulting solution exhibits a special structure that suggests an efficient approach to motion control as well as a planning strategy for energy efficient paths.