Efficient Multi-Agent Exploration with Gaussian Processes

We present a robust and scalable algorithm to enable multiple robots to efficiently explore previously unknown environments. Applications of this algorithm include but are not limited to the exploration of scalar (e.g. concentration of a chemical substance) or vector fields (e.g. direction and intensity of the magnetic field). As opposed to previous works, our algorithm does not require prior knowledge about the shape or size of the environment. Also, its time complexity decreases from cubic to linear in respect to the environment's size. The algorithm employs a Gaussian process model to predict values at still unvisited locations and associates them an uncertainty. Based on a continuously updated map of these predicted values and uncertainties, each robot computes its next movement online by following the local gradient of uncertainty. We have experimentally validated our algorithm with densely measured data of an indoor magnetic field with significant spatial variations. We present a performance comparison of our algorithm with several trajectories. This comparison shows that the estimate computed by our algorithm approaches the true state of the environment faster than these other alternatives.