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SUMMARYThe full-state stabilization scheme is proposed for the control of an underactuated surface vessel with unknown modeling parameters. By knowing only the upper/lower bounds of model parameters, the designed controller is the first one able to globally uniformly asymptotically stabilize all the states of the vessel to zero. The virtual surge velocity control law is first derived, which makes the Lyapunov function at the kinematic level non-increasing, irrelevant to the yaw velocity, leaving a freedom for choosing the virtual yaw velocity control law to stabilize the other state variables. After finishing the design of virtual velocity law, the back-stepping approach and the Lyapunov redesign technique are combined to obtain the actual force/torque control law despite parameter uncertainties. Simulation examples are given to illustrate the effectiveness of the proposed control law, showing that all the states and the control inputs are globally uniformly asymptotically convergent to zero under parameter uncertainties and are globally bounded under unknown external bounded disturbances.

This work investigates the position centroid rendezvous/formation problems of multiple unicycle agents for the first time. By constructing a new output, the unicycle model is converted to canonical normal form via feedback linearisation approach. Then, we propose the centroid rendezvous and the centroid formation control laws, respectively, guaranteeing that all the agents globally meet at the common initial centroid location and the desired geometric pattern centred at the initial centroid. The proposed control laws are distributed, smooth and time-varying, ensuring the internal orientation states and the velocity inputs convergent to some fixed values and zero, respectively. All the results are proved under the communication scenarios of fixed directed balanced graph with a spanning tree. Simulation results verify the effectiveness and the robustness of the proposed control schemes.

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