Physics-informed robotic airflow exploration and mapping with a swarm of mobile robots

Airflow is the key transport mechanism for airborne substances like gas or particulate matter. It is of great interest in many applications ranging from evacuation planning to analyzing indoor ventilation systems. However, accurately determining a spatial map of the airflow is difficult and time-consuming since environmental parameters and boundary conditions are often unknown. This work introduces a novel adaptive sampling strategy for mobile robots. The strategy allows multiple mobile robots with anemometers to autonomously collect airflow measurements and generate a two-dimensional spatial map of the airflow field. Using a Domain-knowledge Assisted Exploration approach, the robots respond in real-time to the measurements already taken and determine the most informative locations online for further measurements. We incorporate the Navier-Stokes Partial Differential Equations to fuse the collected data with model assumptions. By casting the airflow model into a probabilistic framework, we can quantify uncertainties in the airflow field and develop an intelligent, uncertainty-driven exploration strategy inspired by optimal experimental design principles. This strategy combines an estimated uncertainty map with a rapidly exploring random tree path planner. Additionally, using the Navier-Stokes equations allows us to interpolate spatially between measurements in a physics-informed way, enabling us to construct a more accurate airflow map. We implemented and evaluated the proposed concept in simulations and experiments in a laboratory environment, where five mobile robots explore artificially generated airflow fields. The results indicate that our approach can correctly estimate the airflow and show that the proposed adaptive exploration strategy gathers information more efficiently than a predefined sampling pattern.