Model-Based Active Source Identification in Complex Environments

Abstract

We consider the problem of Active Source Identification (ASI) in steady-state Advection-Diffusion (AD) transport systems. Unlike existing bio-inspired heuristic methods, we propose a model-based method that employs the AD-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, a 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 non-convex domains, in simulation and experimentally. This is the first time that PDEs are used for robotic SI in practice.

Distributed State Estimation Using Intermittently Connected Robot Networks

“…To solve Problem II.2, we propose a distributed control framework that concurrently plans robot trajectories that minimize a desired uncertainty metric, e.g., a scalar function of the covariance matrix [18], the Fisher information matrix [48], or the entropy or mutual information of the posterior distribution of x(t) [49], and schedules communication events during which the robots exchange their gathered information and update their beliefs. The schedules of communication events are determined by a correct-by-construction discrete controller that ensures that the communication network is intermittently connected; cf.…”

“…Projection of this path on the workspace of robot r ij yields the path segment p k+T ij . Also, unc(P Ti (t))) denotes an arbitrary uncertainty metric such as a scalar function of the covariance matrix [18], the Fisher information matrix [48], or the entropy or mutual information of the posterior distribution of x(t) [49]. 2 Specifically, in Section IV, we employ the maximum eigenvalue of the posterior covariance as the uncertainty metric.…”

Novel Data Assimilation Algorithm for Nearshore Bathymetry

“…Low-rank approximation can be used to reduce the cost of storing and updating the covariance matrices. Li et al (2015), , Khodayi-mehr et al (2017), and Pham et al (1998) used covariance compression techniques to approximate the covariance matrix P t with a lowrank matrix. This process can be shown as below:…”

“…(3c) is computationally expensive for problems with a large number of observations. To overcome this problem, we take advantage of the fact that the rank of A is smaller than the number of observations and use the Sherman-Morrison-Woodbury formula (Sherman and Morrison 1950;Khodayi-mehr et al 2018a) to compute the inverse of this matrix as below:…”

Online Robot Trajectory Optimization for Persistent Environmental Monitoring

“…The employment of autonomous agents for environmental monitoring has been recognized to be particularly useful for source localization applications [6], [7]. In [8], mobile sensors are controlled to move in order to maximize the information collected required to identify the source of an advective-diffusive environmental field model, implementing, as a matter of fact, an active sensing control strategy.…”