Time-Varying Formation Tracking for Second-Order Multi-Agent Systems Subjected to Switching Topologies With Application to Quadrotor Formation Flying

TLDR

Time‑varying formation tracking for second‑order multi‑agent systems with switching topologies is studied, where followers maintain a predefined formation while tracking a leader. A protocol using neighboring relative information is devised, with necessary and sufficient conditions and a feasibility constraint derived from graph theory; the protocol is designed by solving an algebraic Riccati equation and proven stable via common Lyapunov theory, and applied to a quadrotor target‑enclosing scenario. A numerical simulation and an outdoor experiment demonstrate the effectiveness of the theoretical results.

Abstract

Time-varying formation tracking analysis and design problems for second-order Multi-Agent systems with switching interaction topologies are studied, where the states of the followers form a predefined time-varying formation while tracking the state of the leader. A formation tracking protocol is constructed based on the relative information of the neighboring agents. Necessary and sufficient conditions for Multi-Agent systems with switching interaction topologies to achieve time-varying formation tracking are proposed together with the formation tracking feasibility constraint based on the graph theory. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation, and the stability of the proposed approach is proved using the common Lyapunov stability theory. The obtained results are applied to solve the target enclosing problem of a multiquadrotor unmanned aerial vehicle (UAV) system consisting of one leader (target) quadrotor UAV and three follower quadrotor UAVs. A numerical simulation and an outdoor experiment are presented to demonstrate the effectiveness of the theoretical results.