Design of control policies for spatially inhomogeneous robot swarms with application to commercial pollination

We present an approach to designing scalable, decentralized control policies that produce a desired collective behavior in a spatially inhomogeneous robotic swarm that emulates a system of chemically reacting molecules. Our approach is based on abstracting the swarm to an advection-diffusion-reaction partial differential equation model, which we solve numerically using smoothed particle hydrodynamics (SPH), a meshfree technique that is suitable for advection-dominated systems. The parameters of the macroscopic model are mapped onto the deterministic and random components of individual robot motion and the probabilities that determine stochastic robot task transitions. For very large swarms that are prohibitively expensive to simulate, the macroscopic model, which is independent of the population size, is a useful tool for synthesizing robot control policies with guarantees on performance in a top-down fashion. We illustrate our methodology by formulating a model of rabbiteye blueberry pollination by a swarm of robotic bees and using the macroscopic model to select control policies for efficient pollination.