Providing unpredictable trajectories for patrol robots is essential when coping with adversaries. In order to solve this problem we developed an effective approach based on the known protean behavior of individual prey animals-random zig-zag movement. The proposed bio-inspired method modifies the normal robot's path by incorporating sudden and irregular direction changes without jeopardizing the robot's mission. Such a tactic is aimed to confuse the enemy (e.g. a sniper), offering less time to acquire and retain sight alignment and sight picture. This idea is implemented by simulating a series of fictive-temporary obstacles that will randomly appear in the robot's field of view, deceiving the obstacle avoiding mechanism to react. The new general methodology is particularized by using the Arnold's cat map to obtain the timely random appearance and disappearance of the fictive obstacles. The viability of the proposed method is confirmed through an extensive simulation case study.