Collective dynamics and model verification: Connecting kinetic modeling to data

Control of Stochastic Behaviors in Robotic Swarms using PDE Models

Karthik Elamvazhuthi

Arizona State University


This work addresses a trajectory planning and task allocation problem for a swarm of resource-constrained robots with very limited capabilities. The population dynamics of the robots are modeled as a set of advection- diffusion-reaction partial differential equations. The initial mapping of the spatial distribution of the tasks is then an identification problem for which a small swarm of robots are deployed and a map of the environment is reconstructed using temporal information retrieved from the robots. This information is used for task allocation and trajectory planning. The planning problem is formulated as a PDE-constrained optimization problem, which we solve using techniques from optimal control. The synthesized controls, which consist of the robots' time-dependent velocity field and time-dependent rates of switching tasks, were tested \on microscopic simulations of a commercial pollination scenario to validate our approach.