This paper presents a new technique for exploration and mapping/surveying of underwater infrastructure and/or objects of interest, using multiple autonomous underwater vehicles (AUVs). The proposed method employs rotational potential fields, and extends them for use on multiple vehicles within a three dimensional environment. An inter-vehicle fluid formation is maintained throughout, free of angular constraints (or the need of a virtual vehicle). When an object of interest is approached, the formation is split and follows a smooth trajectory around opposite sides of its boundary. To fully utilise the potential of rotational fields, a unique local 2D-plane is created around every object within the 3D environment, which is employed for boundary coverage. Traditional artificial potential fields are used to guide vehicles towards each object in turn (and maintain the fluid formation), while rotational fields are employed within the local 2D-plane providing a smooth trajectory around opposing sides of every object. Simulation results show the method to be effective, providing a more stable trajectory. Comparison with the standard technique shows that the formation is maintained throughout and overall journey time is significantly reduced using this method. © 2016 IEEE.