Decentralized control of mobile robotic sensors: Vicsek´s model with cosine similarity measure

We investigate the control of a team of randomly heading mobile robots to reach asymptotic consensus for almost sure. Vicsek´s model is based on the state of an agent and its neighbours. The inspiration from Vicsek´s model leads to a locally computed nearest neighbour rule. In the nearest neighbour rule, a mobile robotic sensor always assigns an equal weighting factor to itself and every nearest neighbour coming under its communication range. We consider Salton´s cosine similarity measure among the nearest neighbours of a mobile robotic sensor and the nearest neighbours are not always equally weighted. Consequently, some of the nearest neighbour mobile robots become influential and play an effective role in reaching a consensus value. After introducing the similarity measure among the nearest neighbours, we have compared the obtained simulation results with that of simple nearest neighbour rule. We conclude that the algorithm becomes fast after including the similarity measure among the nearest neighbours of a mobile robot.