  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.
