Effect of random walk methods on searching efficiency in swarm robots for area exploration

The objective of area exploration is to traverse the area effectively and random walk methods are the most commonly used searching strategy for swarm robots. Existing research mainly compares the effectiveness of various random walk methods through experimental verification, which has relatively large limitations. In order to make the application of the random walk methods more convenient, this paper quantitatively analyzes the searching efficiency (SE) of random walk methods. Firstly, the formula of the mean square displacement (MSD) of the robot position is given, and it is shown that the mean and the variance of the random step length are the factors that affect the SE. In addition, in order to produce the suitable step length, a truncated random walk method is constructed to make the generated step lengths follow a given distribution and the step lengths are within a specified range, thereby improving the SE. Thirdly, the correlations between the step length threshold (SLT), the area of the region, and the number of robots are provided based on MSD and truncated random walk method. When the area of region and the number of robots are fixed, there exists a SLT. When the expectation of the step length is greater than SLT, the swarm robots can achieve the highest SE. The area exploration task of swarm robots are carried out in simulation experiments and the coverage ratio is used to evaluate the SE of each random walk method. The experimental results show that when the area and the number of robots are given, there exist an optimal step length, which can enable the robots to achieve the optimal search.