This correspondence presents a novel online trajectory-planning method for the autonomous robotic interception of moving targets in the presence of dynamic obstacles, i.e., position and velocity matching (also referred to as rendezvous). The proposed time-optimal interception method is a hybrid algorithm that augments a novel rendezvous-guidance (RG) technique with the velocity-obstacle approach, for obstacle avoidance, first reported by Fiorini and Shiller. The obstacle-avoidance algorithm itself could not be used in its original form and had to be modified to ensure that the online planned path deviates minimally from the one generated by the RG algorithm. Extensive simulation and experimental analyses, some of which are reported in this correspondence, have clearly demonstrated the tangible time efficiency of the proposed interception method.