Formation control of multi-agent thermal systems to render distributed temperature patterns

This study investigates a temperature-based formation control scheme for a group of thermal agents. The formation patterns are obtained from a numerical solution of Poisson’s Heat Equation in 2D, generating the desired temperature values for a set of cells of a decomposed solid material. The agents were modeled as first-order linear systems based on the behavior of flexible thermoelectric devices (FTED). Using a complete inter-agent communication topology and assigning leader agents, a formation scheme is designed to converge to the formation pattern and satisfy the inter-agent temperature offsets. It is proven that the formation errors converge exponentially to zero with the existence of at least one leader. The approach is demonstrated by numerical simulations and experimental work using FTED as a proof of concept for applications in immersive virtual or augmented reality systems, medical rehabilitation, robotics, etc.