Steerable catheters, as one type of continuum robot, has been popularly used to reach targets to treat atrial fibrillation. Its tip orientation relative to the surface normal of anatomy affects the ablation efficiency and lesion volume. Traditional catheters with a constant deflection have to rely on the reaction force from the tissue to reach targets, and their tip orientation capability is always limited. To overcome this challenge, we propose a miniaturized tendon actuated continuum robot with asymmetric contact-aided compliant mechanisms (CCMs) to generate asymmetric bends. It can adapt to the confined space and improve the tip orientation capability. The general configuration with the customized contact-aided segments and spatial arrangements is investigated. A mechanical model considering self-contacts and tendon interactions is built to describe free bends and constrained bends. A task-oriented optimization based on the mechanical model is implemented to find the best asymmetric configuration with unevenly distributed CCMs. Experiments are carried out to validate the proposed design, model, and optimization. Comparisons of continuum robots with and without CCMs by experiments and simulation demonstrate its potential advantages to improve the deflection and tip orientation in the confined space.