Swarming with mixed position and heading based neighboring interactions

Previously, we proposed a topological-based swarming model in which agents probabilistically decide which other agents to interact with based on the proximity of positions of agents. Agents then average their direction with the directions of the agents they have interacted with. In this paper, we improve the model mentioned-above by taking the influence of similarity of directions into consideration, and the former model can be considered as a special case of this model here. We propose a probabilistic method which depends on both proximity of agents´ positions and similarity of agents´ moving directions. And agents are more likely to form links with those agents who carry a similar direction to theirs and those agents who are proximal to them. We show that there exits a non-zero positive lower bound of the selection probability, and the system can be connected in probability, which ensures the system´s achievement of swarming. And by simulations, it is shown that the rate of getting alignment exhibit a strong correlation with the parameters of the system which are weighting factor, neighborhood size, proximity factor and similarity factor.