This paper introduces a new design for the control of the unconstrained attitude of an underwater mobile robot, dedicated to exploration of karstic environment. The approach followed in this study considers a quaternion formalism and proposes a dynamic control design that copes with the classic two-steps Lyapunov and Backstepping design, that remains within the quaternion formalism. Hence the control expression considers quaternion expressions without (as classically done in literature) requiring the decomposition of the quaternion into vectors and angle, which heavies the control expression and may introduce singularities. This control is then experimented on the Cube robot, showing the performance of the method.