Spatial microscopic modeling of collective movements in multi-robot systems: Design choices and calibration

Despite the strong increase in available computational power enabling an unprecedented level of realism in simulation, modeling robotic systems at higher abstraction level remains crucial to efficiently design robot controllers and analyze their properties. This is especially true for multi-robot systems, with their high computational complexity due to the numerous interactions among individual robots. While multiple contributions in the literature have proposed approaches leading to highly abstracted and therefore computationally efficient models, often such abstractions have been obtained with strong assumptions on the underlying spatiality of the system behavior (e.g., well-mixed system, diffusive system). In this work, we address the modeling of an arbitrary collective movement involving the displacement of a robot ensemble along a certain trajectory overlapped with continuous interactions among the robotic members. Without loss of generality, we have focused our modeling effort on a flocking case study, as a prominent and well-known example of collective movement. We investigate our case study at the microscopic level while leveraging a more faithful submicroscopic model (implemented through a high-fidelity robotic simulator) as ground-truth. More specifically, we illustrate multiple choices for designing and calibrating such microscopic models, so that their faithfulness with the underlying submicroscopic model of the same physical system is preserved. Such effort has produced concrete implementations of three different microscopic models for the same case study, all taking into account the spatiality of the collective movement. We find that all three microscopic models produce quantitatively accurate estimations for our flocking case study. As they rely on different underlying assumptions and modeling techniques, the choice between them is a trade-off between the computational cost, the modeling effort, the metrics considered to evaluate their faithfulness, and the subsequent usage (e.g., control design, system property analysis, control code prototyping).