Coverage path planning (CPP) algorithms customize an autonomous robot's trajectory for various applications. In surveillance and exploration of unknown environments, random CPP can be very effective in searching and finding objects of interest. Robots with random-like search algorithms must be unpredictable in their motion and simultaneously scan an uncertain environment, avoiding intruders and obstacles in their path. Inducing chaos into the robot's controller system makes its navigation unpredictable, accounts for better scanning coverage, and avoids any hurdles (obstacles and intruders) without the need for a map of the environment. The unpredictability, however, will come at the cost of increased coverage time. Due to the associated challenges, previous studies have ignored the coverage time and focused instead on the coverage rate only. This letter establishes a novel method that addresses the coverage time challenge of chaotic path planners. The method here combines the properties of two chaotic systems and manipulates them to achieve a fast coverage of the environment. The outcome has been a technique that can fully cover an area in at least 81% less time compared to state-of-the-art methods.