This technical brief summarizes and extends our recently introduced control framework for stochastically allocating a swarm of robots among boundaries of circular regions. As in the previous work, a macroscopic model of the swarm population dynamics is used to synthesize robot control policies that establish and maintain stable predictable team sizes around region boundaries. However, this extension shows that the control strategy can be implemented with no robot-to-robot communication. Moreover, target team sizes can vary across different types of regions, where a region's type is a subjective characteristic that only needs to be detectable by each individual robot. Thus, regions of one type may have a higher equilibrium team size than regions of another type. In other work that predicts and controls stochastic swarm behaviors using macroscopic models, the equilibrium allocations of the swarm are sensitive to changes in the mean robot encounter rates with objects in the environment. Thus, in those works, as the swarm density or number of objects changes, the control policies on each robot must be retuned to achieve the desired allocations. However, our approach is insensitive to changes in encounter rate and therefore requires no retuning as the environment changes. In this extension, we validate these claims and show how the convergence rate to the target equilibrium allocations can be controlled in swarms with a sufficiently large free-robot population. Furthermore, we demonstrate how our framework can be used to experimentally measure the rates of robot encounters with occupied and unoccupied sections of region boundaries. Thus, our method can be viewed both as an encounter-rate-independent allocation strategy as well as a tool for accurately measuring encounter rates when using other swarm control strategies that depend on them.

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