In robot-assisted procedures, the surgeon’s ability can be enhanced by navigation guidance through the use of virtual fixtures or active constraints. This paper presents a real-time modeling scheme for dynamic active constraints with fast and simple mesh adaptation under cardiac deformation and changes in anatomic structure. A smooth tubular pathway is constructed which provides assistance for a flexible hyper-redundant robot to circumnavigate the heart with the aim of undertaking bilateral pulmonary vein isolation as part of a modified maze procedure for the treatment of debilitating arrhythmia and atrial fibrillation. In contrast to existing approaches, the method incorporates detailed geometrical constraints with explicit manipulation margins of the forbidden region for an entire articulated surgical instrument, rather than just the end-effector itself. Detailed experimental validation is conducted to demonstrate the speed and accuracy of the instrument navigation with and without the use of the proposed dynamic constraints.