Styled-Velocity Flocking of Autonomous Vehicles: A Systematic Design

This paper develops a measure-theoretic approach for generating the collective behavior of flocking of planar autonomous vehicles under all-to-all communication scheme. To obtain flocking protocol, we formulate the notion of state of styled-velocity flocking for the target state of a design problem instead of considering solution-ansatzes. This notion captures a broader class of flocking behaviors of non-parallel motions, as well as embodies the two important performances of cohesion maintenance and collision avoidance. To pose a control design problem, a measure-valued transition equation is obtained to induce an auxiliary one-body continuum-model from the exact multi-body particle-model of the collective system. The design problem is then formulated on the auxiliary continuum-model, and a systematic design procedure is presented. The state of styled-velocity flocking of the particle-model under the obtained flocking protocol is then verified with an important result on the continuous dependence on initial data of solutions of the measured-valued transition equation. Application to elliptical flocking of mobile robots is presented to illustrate the novelty of the presented theory.