A leader-follower synchronization output feedback control scheme is presented for the ship replenishment problem where only positions are measured. No mathematical model of the leader ship is required, and the control scheme relies on nonlinear observers to estimate velocity and acceleration of all ships to realize the feedback control law. The scheme yields semi-global uniform ultimate boundedness of the closed-loop errors. The bound is a function of the main ship acceleration, and under the assumption of zero main ship acceleration the closed-loop errors are semi-globally exponentially converging. The results are verified through experiments on a model-scale ship. r

Abstract-In this brief, we consider output feedback tracking of ships with position and orientation measurements only. Ship dynamics are highly nonlinear, and for tracking control, as opposed to dynamic positioning, these nonlinearities have to be taken into account in the control design. We propose an observer-controller scheme which takes into account the complete ship dynamics, including Coriolis and centripetal forces and nonlinear damping, and results in a semi-globally uniformly stable closed-loop system. Furthermore, a gain tuning procedure for the observer-controller scheme is developed. Experimental results are presented where the observer-controller scheme is implemented onboard a Froude scaled 1:70 model supply ship. The experimentally obtained results are compared with simulation results under ideal conditions and both support the theoretical results on semi-global exponential stability of the closed-loop system.

AcknowledgementsI am very grateful that prof.dr. Henk Nijmeijer and prof.dr. Kristin Y. Pettersen have given me the opportunity to do my second traineeship in Norway on the subject of synchronization control of ship rendezvous operations. I like to thank prof.dr. Kristin Y. Pettersen for her hospitality, her enthusiasm, her advice and comments and all the other things she arranged for me during my stay in Norway. This applies also t o siv.ing. Erik Kyrkjebm and siv.ing. Roger Skjetne, who helped me a lot during this project. Every question I had, I could ask to one of them. It has been a great pleasure to work in this group. I like to thank prof.dr. Henk Nijmeijer for his very nice contribution on the CAMS article, which was maybe the finishing touch we needed. I should thank all the people in my office as well. Espen, Andreas and Anne Marthine for their friendship and nice talks during the lunch and dinner. AbstractThis report presents experimental results on rendezvous control of ships using an external synchronization control scheme. I n particular, a leader-follower synchronization scheme for underway replenishment of ships is verified through a back-to-back comparison between experimental results and ideal simulations. The experiments illustrate that the synchronization controller yields exponential convergence of the closed-loop errors for position keeping, and uniform ultimate boundedness of the closed-loop errors during trajectory trac~ing. The gain tuning process is motivated, and the effects of iiieasireiiien: noise and environmental disturbances on the control scheme performance are discussed. To avoid or shorten port time it is necessary for ships to do underway replenishment (UNREP) at sea. The primaty aim of m UNREP operstior! is the safe de!ivegf of the maximun? amouat of cargo and f~e ! from one ship to another ship in the minimum amount of time. There are two methods to replenish a ship, vertical replenishment (VERTREP) and connected replenishment (CONREP). During VERTREP operations helicopters are used to transport the cargo from the supply vessel or tanker to the replenished ship and vice versa. The ships are in close proximity, or miles apart depending on the tactical situation for military purposes and economic aspects for civil purposes. During connected replenishment (CONREP) operations, two ships steam side by side and hoses and lines are used to transfer fuel, cargo, ammunition or personnel from one ship to the other. I n appendix A some background information is given about full scale replenishment operations. ContentsAn external synchronization scheme was recently proposed by Kyrkjebm and Pettersen (2003) to dynamically control the supply ship to the position and velocity of a desired trajectory created on basis of the actual position of the replenished ship during CONREP operations. The trajectory for the supply ship is oniy based on the actual position of the replenished ship, which means that the supply ship is controlled with respect to the actual position of the main ship. This i...