LAUSR

This article presents novel distributed prescribed performance control for three‐dimension (3D) time‐varying formation of multiple underactuated autonomous underwater vehicles (AUVs) with uncertain dynamics and unknown disturbances. Different from the regular prescribed performance function, a novel form of prescribed performance function is proposed such that the time desired for the formation errors of AUVs to reach and stay within the prescribed tolerant band can be preset exactly and flexibly. Furthermore, a simple error mapping function is constructed to transform the formation errors constrained by the prescribed performance into the unconstrained transformed errors. With the aid of radial basis function neural networks, the uncertain item lumped by uncertain dynamics and unknown disturbances of AUVs is artfully converted into a linearly parametric form with only a single unknown parameter. Based on the above, a robust adaptive 3D time‐varying formation control law of AUVs is developed incorporating a second‐order sliding mode differentiator into the backstepping method. The theoretical analysis and simulation results validate our developed formation control scheme.