Flexible, ergonomically enhanced surgical robots have important applications to transluminal endoscopic surgery, for which path-following and dynamic shape conformance are essential. In this paper, kinematic control of a snake robot for motion stabilisation under dynamic active constraints is addressed. The main objective is to enable the robot to track the visual target accurately and steadily on deforming tissue whilst conforming to pre-defined anatomical constraints. The motion tracking can also be augmented with manual control. By taking into account the physical limits in terms of maximum frequency response of the system (manifested as a delay between the input of the manipulator and the movement of the end-effector), we show the importance of visual-motor synchronisation for performing accurate smooth pursuit movements. Detailed user experiments are performed to demonstrate the practical value of the proposed control mechanism.