This paper introduces a novel fan-out model that improves accuracy over previous models. The commonly used models rely on neglect time, the time an agent operates independently, which confounds both human and robot abilities. The proposed model separates neglect time into two functionally distinct concepts: the time a robot can operate self-sufficiently, and the time a human estimates the robot can do so. Previous research indicates fan-out is often overestimated. This work explains why robot ability provides an upper bound to fan-out, but that actual achieved fan-out is influenced by both the human and robot abilities. We conduct a study to validate this new model and show improved performance over the two most common fan-out models. The results show that both previous models overestimate as predicted. Using the new fan-out model, we show that as the difference between human estimation and robot abilities grows, the actual fan-out will fall further from the upper bound potential fan-out. By including assessments of both the robotic and human elements, the new model provides a more nuanced understanding of the dynamics at play and the factors involved in scaling Human Multi-Robot Teams.

Scalability of human multi-robot teams is quickly becoming a crucial area of research as autonomous systems become more capable and sophisticated. A key research challenge is developing predictive measures of scalability, such as fan-out. This paper presents the results from a study that confirms the improved accuracy of a novel fan-out model over two previous models. It utilizes a new test domain to assess scalability and investigate the role of uncertainty through a variety of complexities driven by environmental factors, robot behaviors, and human-robot interactions. Our analysis highlights potential enhancements to optimize model accuracy across all the models. Finally, we show that when calibrating for measurement error, the new model is bounded, which sets it apart from previous models that are unbounded. The new model provides a more nuanced understanding of the dynamics at play and the factors involved in scaling Human Multi-Robot Teams under uncertainty.