Using Fuzzy Logic to Design Separation Function in Flocking Algorithms

Flocking algorithms essentially consist of three components: alignment, cohesion, and separation. To track a desired trajectory, the flock center should move along the desired trajectory, and thus, the fourth component, navigation, is necessary. The alignment, cohesion, and navigation components are well implemented through consensus protocols and tracking controls, while the separation component is designed through heuristic-based approaches. This paper proposes a fuzzy logic solution to the separation component. The TS rules and Gaussian membership functions are used in fuzzy logic. For fixed network flocking, a standard stability proof by using LaSalle's invariance principle is provided. For dynamic network flocking, a Filipov solution definition is given for nonsmooth dynamics. Then, a LaSalle's invariance principle for nonsmooth dynamics is used to prove the stability. A group of mobile robots with double integrator dynamics is simulated for the flocking algorithms in a 2-D environment.