In this paper we present a strategy that allows a swarm of autonomous tugboats to cooperatively move a large object on the water. The two main challenges are: (1) the actuators are unidirectional and experience saturation; (2) the hydrodynamics of the system are difficult to characterize. The primary theoretical contribution of the paper addresses the first challenge. We present a tracking controller and force allocation strategy that, despite actuator limitations, result in asymptotically convergent tracking for a certain class of reference trajectories. The primary practical contribution is the introduction of a set of adaptive control laws that address the second challenge by compensating for unknown, and difficult to measure, hydrodynamic parameters. Experimental verification of the controllers is presented using a 1:36 scale model of a U.S. Navy ship, inside the Naval Academy's unique 380 ft testing tank.