Collective motion with shared environment map

This chapter considers motion of the group of robots following common environment map, which is defined by the terrain or certain potential field, and stresses the differences between collective and swarm dynamics. The discourse is illustrated by probabilistic search algorithms and the methods of obstacle and collision avoidance based on attraction/repulsion potentials. In contrast to the activity of the agents in the homogeneous environment, where the agents are not restricted in their motion, sensing, and communication abilities, swarm behavior in heterogeneous environments is restricted by the environmental states, which can accelerate or slow down the agents’ movement, and by possible obstacles, which bound the agents’ mobility. Following the model of swarm dynamics based on active Brownian motion, the first restriction is represented by nonlinear friction that can obtain both positive and negative values with respect to the environmental topography, and the second - by additional external potential.