Towards Predicting Collective Performance in Multi-Robot Teams

TL;DR

This paper addresses the challenge of predicting collective performance in multi-robot teams by introducing a dimensionless-variable framework that condenses high-dimensional MR-MTT parameters into universal, scale-free descriptors. It combines two time-dependent performance models (exponential and sigmoid) with Buckingham Pi-based dimensionless forms to predict metrics like OSPA and EI, using Adam-based learning to jointly optimize the dimensionless structure and model parameters. Across multiple MR-MTT algorithms and datasets, the approach reveals consistent dimensionless relationships, notably the primacy of the target-to-robot ratio and sensing radius, and demonstrates strong generalization for interpolation and extrapolation. The work offers a principled, generalizable method to analyze, compare, and optimize MR-MRS deployments, facilitating faster design decisions and robust performance forecasting in diverse environments.

Abstract

The increased deployment of multi-robot systems (MRS) in various fields has led to the need for analysis of system-level performance. However, creating consistent metrics for MRS is challenging due to the wide range of system and environmental factors, such as team size and environment size. This paper presents a new analytical framework for MRS based on dimensionless variable analysis, a mathematical technique typically used to simplify complex physical systems. This approach effectively condenses the complex parameters influencing MRS performance into a manageable set of dimensionless variables. We form dimensionless variables which encapsulate key parameters of the robot team and task. Then we use these dimensionless variables to fit a parametric model of team performance. Our model successfully identifies critical performance determinants and their interdependencies, providing insight for MRS design and optimization. The application of dimensionless variable analysis to MRS offers a promising method for MRS analysis that effectively reduces complexity, enhances comprehension of system behaviors, and informs the design and management of future MRS deployments.

Figures (11)

• Figure 1: Comparison of steady state median OSPA errors across 10 trials for various distributed control algorithms, considering a range of robot numbers and 50 static targets.
• Figure 2: The black points represent the median OSPA value from the dataset with a batch size of 10 over time. The red lines illustrate the fitting results using a sigmoid function.
• Figure 3: Comparative analyses of the variables $a$, $b$, and $c$ from the Exponential fitting method, and $L$, $k$, and $d$ from the sigmoid fitting method, against the target number $n_t$. The data is from ACO method.
• Figure 4: Comparison between groundtruth OSPA, sigmoid fitted OSPA and predicted OSPA via dimensionless variable from PSO method.
• Figure 5: Comparison between groundtruth OSPA, exponential fitted OSPA and predicted OSPA via dimensionless variable from SA method.