Abstract: Formation control is a key problem in the field of multi-robot cooperative control. Considering the complexity of the practical environment, the research of formation control for heterogeneous multi-robot systems is more significance in engineering. Furthermore, when heterogeneous multi-robot systems exist time-delays, the consensus analysis of the different order robots is more difficult. Concerning the above problems, a formation control algorithm for heterogeneous multi-robot systems based on the consensus theory is proposed. Considering two cases of the zero time-delay and the fixed time-delay, the formation control problem of heterogeneous multi-robot systems based upon leader-following model is transformed into a stability problem by using the consensus theory. A necessary and sufficient condition for the formation control problem is obtained by matrix analysis and Routh-Hurwitz theorems. In addition, a Lyapunov-Razumikhin function is constructed. By untilizing the Newton-Leibniz formula and the Lyapunov theorem, the sufficient condition for formation control of fixed time-delay systems is presented. Simulation results show that this consensus algorithm can make the heterogeneous multi-robot system with communication time-delays realize formation precise control.

Key words: formation control, time-delay, heterogeneous multi-robot system, consensus, leader-following

摘要： 编队控制是多机器人协同控制领域研究的重点问题。考虑实际复杂环境，对异构多机器人系统的编队控制研究更具工程意义。再者，当异构多机器人编队系统存在通信时延时，同时对系统中不同阶机器人进行一致性分析的难度增大。针对以上问题，提出一种基于一致性理论的异构系统编队控制算法。考虑零时延与固定时延两种情况，首先，利用一致性思想将领航跟随者模式下的异构多机器人系统编队控制问题转换为稳定性问题。然后，根据矩阵分析与Routh-Hurwitz定理，推导出零时延系统实现编队控制的充要条件。进一步构造Lyapunov-Razumikhin函数，利用Newton-Leibniz公式与Lyapunov定理，推导出固定时延系统实现编队控制的充分条件。仿真结果表明：基于一致性算法的异构多机器人系统能够实现相互通信时延条件下的编队精确控制。

关键词: 编队控制, 时延, 异构多机器人系统, 一致性, 领航跟随者