Proc. 41st IEEE Conf. Decision and Control, 2002 Stabilization and Coordination of Underwater Gliders Pradeep Bhatta and Naomi Ehrich Leonard 1 Department of Mechanical and Aerospace Engineering Princeton University Princeton, NJ 08544 USA pradeep@princeton.edu, naomi@princeton.edu Abstract An underwater glider is a buoyancy-driven, fixed- wing underwater vehicle that redistributes internal mass to control attitude. We examine the dynamics of a glider restricted to the vertical plane and derive a feedback law that stabilizes steady glide paths. The control law is physically motivated and with the appro- priate choice of output can be interpreted as providing input-output feedback linearization. With this choice of output, we extend the feedback linearization approach to design control laws to coordinate the gliding motion of multiple underwater gliders. 1 Introduction Underwater gliders are designed to be efficient and reliable so that when used in a network they can provide spatially and temporally dense ocean sampling data over long time periods [1]. An underwater glider is distinguished by a buoyancy engine, internal mass re- distribution, fixed wings and the isolation of moving parts from the sea environment. The buoyancy engine changes the mass or the volume of the vehicle and thus controls the net buoyant force on the vehicle. The mass distribution system shifts internal mass and controls the attitude of the vehicle. A number of underwater gliders are operational [2, 11, 12]. Our laboratory-scale underwater glider ROGUE, shown in Figure 1.1, uses four servo and sy- ringe pairs on board to admit and expel water, which in turn control vehicle mass as well as mass redistribu- tion [5, 4]. The control and coordination problems are challenging because gliders are underactuated and the internal control introduces important but subtle cou- pling. In this paper we investigate control of a glider and coordination of multiple gliders for dynamics re- stricted to the vertical plane. The nominal glider mo- 1 Research partially supported by the Office of Naval Research under grants N00014–98–1–0649 and and N00014-01-1-0526, by the National Science Foundation under grant CCR–9980058 and by the Air Force Office of Scientific Research under grant F49620- 01-1-0382. Figure 1.1: Ballast tanks in ROGUE tion in the vertical plane is a sawtooth motion in which the glider switches between a dive (heavy and pitched down) and an upwards glide (light and pitched up). Certain of these glide paths are steady motions for the glider and these are therefore important for low-energy trajectories. Our starting point in §2 is the underwater glider model presented in [8]. In §3 we discuss instability of glide paths when the internal shifting mass is allowed to move around freely inside the vehicle (like instabil- ity in the fuel slosh problem for space vehicles). In §4 we propose a control law which can be interpreted as the realization of a suspension system for the shifting mass. This control law provides input-output lineariza- tion. The minimum phase property is used in §5 to de- sign a control law to stabilize steady glide paths and to provide tracking of desired shifting mass and buoyancy mass trajectories. In §6 this is extended to the problem of stable coordination of multiple vehicles. The feed- back linearization and minimum phase property make it possible to use an approach to coordination intended for fully actuated vehicles. Extension to underactuated vehicles is possible as in the treatment of nonholonomic robots in see Lawton et al [7]. We conclude in §7. p. 1