The autonomous recovery of autonomous underwater vehicles (AUVs) using unmanned surface vehicles (USVs) is a critical prerequisite for achieving surface and underwater collaboration. The existing recovery methods primarily rely on the maneuverability of the AUV to complete the recovery, which significantly impacts the recovery success rate in complex marine environments. In this context, we propose a novel dynamic recovery control scheme based on the designed catamaran USV to recover the AUV actively. The features of the developed recovery controller are threefold: 1) by transforming the dynamic recovery control problem into a trajectory tracking control problem, a dynamic recovery approach is constructed; 2) a novel performance function is incorporated into the $\mathbf{tan}$ -type barrier function to provide the reasonable recovery position and attitude, which ensures that the AUV can be constrained within the range of the recovery cage; and 3) the issues of input saturation, initial speed jump, and external disturbances are addressed by employing auxiliary dynamic system, bioinspired neurodynamics, and disturbance observer, respectively. With the developed controller, the tracking errors can be guaranteed to converge into a small neighborhood of the zero. Finally, both simulation and experimental results are presented to illustrate the effectiveness of the developed recovery control algorithm.