几何约束视角下异构群体队形光滑变换控制方法研究

Flock/crowd formation control technology can enhance cooperation and reliability, thus has many applications in computer animation, robots control, gaming and so on. Aiming to overcome the regularity, smoothness and stability problem of existing methods, an innovative theory for regulated heterogeneous flock formation control based on MPL(Morphing-Powerdiagram-Lloyd) geometry-constrained mechanism is proposed, which employs Morphing technique to generate a series of in-between constrained shapes to impose process control and ensure smoothness, introduces CCCPD(Centroidal Capacity Constrained Power Diagram) theory to calculate the heterogeneous and optimal distribution layout of agents, and presents Lloyd method of Power diagram, that is PD-Lloyd, to perform path planning and obstacle avoiding for agents by solving the variant domain problem caused by multi-constrain-shapes. At the same time, to handle the environment obstacle avoiding problem for the whole flock, a method named path-time domain based moving space modification is put forward in order to preserve certain formation as much as possible while getting round obstacles. Also, according to the autonomous control requirement of individuals in a real flock, an asynchronous and decentralized algorithm of MPL is presented, which can be used for swarm robot formation control and so on. The proposed scheme can generate high quality formation transformation results having characteristics of heterogeneity, smoothness, optimum, regularity, and stability.

群体队形控制可增强群体协作性和可靠性，应用于很多领域。为克服现有形状约束法存在的光滑性、条理性之不足，以及虚拟结构法刚性、控制复杂之限制，本申请提出一种基于MPL(Morphing-Powerdiagram-Lloyd)几何约束机理的受限异构群体队形控制方法：采用Morphing方法生成从源队形变换至目标队形的系列中间约束形状，进行过程控制以保证变换平滑性；引入基于质心的容量限制Power图理论，施加质心限制保证队形优化分布，施加容量限制以符合异构布局；提出Power图下的PD-Lloyd下降法进行群体覆盖路径规划，解决多约束形状导致的变空间域问题以稳定收敛于Power图分布，给出运动空间修正法进行全局环境障碍避免以在避障同时尽可能保持队形；针对群机器人系统自主控制特点，研究MPL方法的异步分散算法以进行分布控制。本方案能产生异构分布、过渡光滑、队形优化、过程整齐、路径条理的精细变换结果。

本课题聚焦于群体队形控制问题，引入几何约束机制，旨在生成高质量的群体队形控制结果。课题深入研究Power图的几何特性，利用容量限制来生成不同大小剖分，从而对群体分布异构性进行建模。针对容量限制Power图计算速度代价高的问题，研究相应的加速生成算法：一是提出了一种精确求解容量限制Power图算法，通过站点权值与容量之间的解析关系，快速求解权值增量，进而加快Power图的生成；二是提出一种常密度下的定点容量限制质心Power图生成算法，通过交替优化质心位置和容量限制，生成定点质心Power图。在此基础上，结合Morphing、Power图和Lloyd方法提出一种异构群体队形控制方法MPL，首先采用Morphing方法生成由初始队形到目标队形的一系列中间约束形状，保证队形变换平滑性；然后引入基于质心的容量限制Power图产生所需的异构分布；最后通过PD-Lloyd路径规划算法进行CCCPD上的覆盖路径规划，实现平滑且条理的变换结果。作为本课题的拓展，进一步将容量限制Power图应用到选址-分配问题，拓展其应用范围。

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