Multi-agent flocking via generalized control algorithms: Existence and properties

In this paper, we propose a class of generalized flocking algorithms based on the Olfati-Saber's results for self-driving multi-agent networks by introducing some metric weighting matrix and leader-agent-related navigation-weighting coefficients, in which the multi-agents are also driven by distributed continuous-time control algorithms that are defined merely by local position and velocity measurements of neighboring multi-agents as usual. It is shown that the concerned multi-agent systems eventually run into what we call the generalized α-lattice flocking by means of the generalized algorithms, while flocking lattice geometries such as direction variation and lattice deformation (say, shrinkage and enlargement) can be achieved by choosing the weighting matrix and the leader agent coefficients. In the process of flocking, the whole multi-agent system satisfies the Reynold's principles of flocking aggregation, collision avoidance and velocity matching, while possible inter-agent collision is also verified by means of the variation-of-constants formula when initially the agents are aggregative too densely.