基于任意参考轨迹的非完整多智能体系统的统一分布式编队控制方法研究

The research project aims to study the unified distributed formation control problem of multiple nonholonomic agent systems with an arbitrary reference trajectory (including fixed, feasible, non-feasible and null ones). Up to now, there exsits no distributed control protocol that can steer a group of nonholonomic agents to form a desired geometric shape and practically track an arbitrary reference trajectory. Therefore, novel distributed control approaches should be developed to make a group of multiple nonholonomic agents tend to a desired geometric shape, and as a whole, track an arbitrary reference trajectory with the formation tracking errors globally uniformly asymptotically convergent to an arbitrary small neighborhood of origin. The research objects include: design unified distributed controllers with all or part of agents knowing the reference trajectory; design unified distributed robust controllers for an uncertain nonholonomic agent group; verify the theoretical results experimentally. The obtained unified formation distributed control schemes of nonholonomic agent systems with an arbitrary reference trajectory, not only can simultaneously solve the formation tracking and the formation stabilization problems, but also can guarantee the nonholonomic agents track a leader with an arbitrary model and motion patten; hence providing new ideas and new approaches for solving the unified distributed formation control problem of multiple nonholonomic agent systems in both the theoretical and the practical aspects.

本项目研究基于任意参考轨迹(包括定常、可行和不可行参考轨迹以及无参考轨迹)的非完整多智能体系统的统一分布式编队控制问题。迄今为止，还没有出现能够保证非完整多智能体系统以期望队形实际跟踪任意参考轨迹的分布式控制算法。项目旨拟研究探索新的分布式控制算法，使得非完整多智能体系统以期望的几何队形跟踪任意参考轨迹，并且保证编队跟踪误差全局一致渐近收敛到原点的任意小邻域内。拟解决的主要问题包括：所有智能体以及仅部分智能体可获得期望参考轨迹时的统一分布式编队控制问题；不确定非完整多智能体系统的统一分布式编队控制问题；控制算法的实验验证。所得到的统一分布式编队控制器不仅可以同时实现非完整系统的编队跟踪和镇定两类控制目标，还可以使非完整多智能体系统编队跟踪具有任意模型和运动模式的领航者。该研究将为非完整多智能体系统的编队控制理论和实际应用提供新的思路和方法。

本项目研究基于任意参考轨迹的非完整多智能体系统的统一分布式编队控制问题。现有非完整多智能体系统的分布式编队算法只能跟踪满足较强激励条件的可行期望轨迹，无法实现任意轨迹的编队跟踪。为此，给出一种可以实现非完整多智能体系统任意轨迹编队跟踪的分布式控制器设计方法。该方法首先为每个非完整智能体设计一个线性虚拟智能体，然后针对线性虚拟智能体系统设计分布式控制律实现任意轨迹的编队跟踪，最后为每个非完整智能体设计局部跟踪控制器跟踪其线性虚拟智能体的状态轨迹。依照上述设计思路分别得到了轮式移动机器人、水面船舶、气垫船和飞行器的分布式编队控制算法。理论分析表明，只要期望轨迹函数的各阶导数有界，基于该方法所设计的分布式控制算法可以保证多个非完整智能体系统以期望的队形跟踪期望的轨迹，并且跟踪误差界的大小可以任意调节。此外，当非完整智能体邻居之间的通讯连接图为合作竞争网络时，深入研究了虚拟线性智能体的动态行为，提出了根圈的概念，发现了区间二部一致性等新的网络动态行为。所得结果在自行设计的多轮式移动机器人平台上进行了编队控制实验，验证了所提出的设计方法的有效性。