Model-Based Active Source Identification in Complex Environments

In this paper, we consider the problem of Active Source Identification in steady-state advection-diffusion (AD) transport systems. Unlike existing bioinspired heuristic methods, we propose a model-based approach that employs the AD-partial differential equation (PDE) to capture the transport phenomenon. Specifically, we formulate the source identification (SI) problem as a PDE-constrained optimization problem in function spaces. To obtain a tractable solution, we reduce the dimension of the concentration field using Proper Orthogonal Decomposition and approximate the unknown source field using nonlinear basis functions, drastically decreasing the number of unknowns. Moreover, to collect the concentration measurements, we control a robot sensor through a sequence of waypoints that maximize the smallest eigenvalue of the Fisher Information matrix of the unknown source parameters. Specifically, after every new measurement, an SI problem is solved to obtain a source estimate that is used to determine the next waypoint. We show that our algorithm can efficiently identify sources in complex AD systems and nonconvex domains, in simulation and experimentally. This is the first time that PDEs are used for robotic SI in practice.