This paper addresses the path-planning challenge for very large-scale robotic systems (VLSR) operating in complex and cluttered environments. VLSR systems consist of numerous cooperative agents or robots working together autonomously. Traditionally, many approaches for VLSR systems are developed based on Gaussian mixture models (GMMs), where the GMMs represent agents' evolving spatial distribution, serving as a macroscopic view of the system's state. However, our recent research into VLSR systems has unveiled limitations in using GMMs to represent agent distributions, especially in cluttered environments. To overcome these limitations, we propose a novel model called the skew-normal mixture model (SNMM) for representing agent distributions. Additionally, we present a parameter learning algorithm designed to estimate the SNMM's parameters using sample data. Furthermore, we develop two SNMM-based path-planning algorithms to guide VLSR systems through complex and cluttered environments. Our simulation results demonstrate the effectiveness and superiority of these algorithms compared to GMM-based path-planning methods.

翻译：本文针对在复杂杂乱环境中运行的超大规模机器人系统（VLSR）的路径规划挑战。VLSR系统由众多自主协同工作的智能体或机器人组成。传统上，许多VLSR系统方法基于高斯混合模型（GMM）开发，其中GMM代表智能体不断演化的空间分布，作为系统状态的宏观视图。然而，我们近期对VLSR系统的研究发现，使用GMM表示智能体分布存在局限性，特别是在杂乱环境中。为克服这些局限，我们提出了一种称为偏态正态混合模型（SNMM）的新模型来表示智能体分布。此外，我们提出了一种参数学习算法，利用样本数据估计SNMM的参数。更进一步，我们开发了两种基于SNMM的路径规划算法，引导VLSR系统穿越复杂杂乱环境。仿真结果表明，与基于GMM的路径规划方法相比，这些算法具有有效性和优越性。