Flexible serpentine manipulators are widely used in surgical robots as it can be operated inside the patient's body cavity by backbone bending. However, during the bending the manipulator sweeps over a region, where sensitive organs may locate. This raises the safety concern. In this paper, a motion planning algorithm focusing on minimize the sweeping area for flexible serpentine manipulators is presented. Particularly, a three dimensional backward average neural dynamic model (BANDM) is proposed to build minimum sweeping area planning field in the configuration space of the serpentine manipulator. Given a target position, the motion sequence is generated automatically based on the established planning field. The simulations and experimental results validate the effectiveness and superiority of the proposed planning approach over conventional planning algorithms in terms of sweeping area with keeping target reach and obstacle avoidance.