Evaluation and Modification of Kinetic Gas Collision Theory as Applied to Encounter Rate Dynamics for Multi-Robot Groups and Robot Swarms

Abstract Robots encountering other robots in a group can be beneficial, e.g., to exchange information, or detrimental, e.g., obstructing one another from operating. Kinetic gas theory (KGT) provides a statistical mechanical analysis of the collision rate between molecules. KGT has been applied to model robot encounter rates but there has been some inconsistency in how it has been applied to robot groups. There is a nine order of magnitude difference in size between a typical robot and molecule, so it is not a surprise that some adjustments may need to be made when considering robots instead of molecules. This work develops a model in detail by applying KGT, articulates limitations of applying this theory to robots, highlights inconsistencies in how it has been previously applied to robots, and suggests modifications to the model. A simple numerical study is also shown to validate the model and highlight the effect of differences in the implementation. The most important gap that this research has identified is the need to collect data on the magnitude and direction distribution of robots' velocities. Robots move and behave differently than gas molecules, whose velocity magnitude follow a Boltzmann distribution. A second major result is the connection of the KGT-based model developed in this work and previous research on robot encounter rate which independently arrived at the same relationship between robot size, number of robots, and encounter rate.