Biologists proposed the tau theory to explain how animals control their motion using visual feedback for different tasks including landing and perching. Tau theory is based on a concept called time-to-contact, which is the required time to contact an object if the current velocity is maintained. Recently, tau theory has been applied to control robots' motion for similar tasks such as perching, docking, braking, or landing. However, existing tau theory can only work for the case with zero contact velocity. Some tasks such as perching actually require a non-zero contact velocity to make gripping mechanisms work. To address this problem, we extend the tau theory by proposing a two-stage strategy in one dimensional space to generate the reference trajectory for time-to-contact. Moreover, we propose a new coupling strategy to deal with the motion in three dimensional space. Simulation results demonstrate the effectiveness of proposed two-stage and coupling strategies. Moreover, we leverage a featureless method to estimate the time-to-contact from image sequences and implement it on a mobile robot platform. Experimental results also demonstrate that the non-zero contact velocity can be accomplished using onboard vision feedback. The research presented in this paper can be readily applied to control the motion of flying robots for perching with visual feedback.