A Novel Multivariate Skew-Normal Mixture Model and Its Application in Path-Planning for Very-Large-Scale Robotic Systems

TL;DR

This paper proposes a novel model called the skew-normal mixture model (SNMM) for representing agent distributions and develops two SNMM-based path-planning algorithms to guide VLSR systems through complex and cluttered environments.

Abstract

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.

Figures (9)

• Figure 1: Left: Samples ($N = 300$) generated according to the underlying 2-component BRF-SNMM distribution are deployed with the obstacle in the workspace. The red points indicate the samples, and the gray rectangle indicates the obstacle. Right: Comparison of parameter learning performances. The NLLs are generated by different approaches for different values of $N_C$.
• Figure 2: The path-planning problem for VLSR systems in the simple artificial forest environment (Forest-I simulation). Left: The red points indicate the initially deployed agents, and the black circles represent the “trees” in the forest. Right: The desired agents’ PDF is shown, where the white areas are occupied by “trees”.
• Figure 3: Snapshots of the trajectory of agents and corresponding PDFs generated by the SNMM-DI approach in the Forest-I simulation.
• Figure 4: Snapshots of the trajectory of agents and corresponding PDFs generated by the SNMM-APF approach in the Forest-I simulation.
• Figure 5: Snapshots of the trajectory of agents and corresponding PDFs generated by the GMM-APF approach in the Forest-I simulation.

Theorems & Definitions (2)

• Definition 1: Fundamental Skew-Normal Distribution
• Definition 2: Bernoulli-Random-Field based Skew-Normal Distribution