Control of fully actuated ocean vehicles under stochastic environmental loads in three dimensional space

• All existing works on control of ocean vehicles treat environmental loads as deterministic.
• Stochastic equations of motion of ocean vehicles for control design are derived.
• New robust adaptive controllers are designed for ocean vehicles under stochastic loads.
• The tracking errors converge to an arbitrarily small neighborhood of the origin in probability.

Although environmental loads induced by waves, wind, and ocean currents on ocean vehicles are naturally stochastic, all existing works on controlling these vehicles treat the loads as deterministic. This treatment deteriorates the control performance or even results in an unstable closed loop system in a practical implementation. This paper presents a method to design controllers that force a fully actuated ocean vehicle under stochastic environmental loads to track a reference trajectory in three dimensional space. The control design is based on several recent results developed for stability and control of stochastic systems, and backstepping and Lyapunov׳s direct methods. The modified Rodrigues parameters are used for the attitude representation of the vehicle to reduce singularities in comparison with the use of Euler-angles and Rodrigues parameters. Simulations on an omni-directional intelligent navigator illustrate the results.