A Kinetic Theory of Encounter-Based Information Propagation in Multi-Robot Systems

Multi-robot systems cannot assume persistent network connectivity. We study this problem through target tracking, where performance depends on how quickly target information is sensed, transported through the team, and used before it becomes stale. When robots exchange information only through physical encounters, tracking becomes a kinetic information-transport problem: robot motion induces encounters, encounters carry target-state estimates, information age determines staleness, and stale information produces tracking error. This paper develops a kinetic theory of encounter-based information propagation and identifies three limits. The first is an access limit -- information cannot support team-level coordination unless it spreads beyond the robots that sensed it. The second is a staleness limit -- even propagated information loses value as the target moves. The third is a geometry limit -- when target motion outpaces information transport, tracking error approaches a saturation regime where communication improvements alone have diminishing returns. We evaluate the theory through large-scale simulations varying team size, operating area, communication range, and target speed. Results support the proposed access-staleness-geometry decomposition: communication coverage governs the access transition; once information is accessible, tracking error is shaped by target displacement; and this response is locally linear in restricted regimes but nonlinear over broader ranges because of sensing refreshes and bounded geometry. Across controlled sweeps and joint variation, the derived access and staleness coordinates reliably describe tracking performance. Together, these results establish a kinetic-theoretic framework for predicting and designing encounter-based multi-robot systems.