Source seeking arises in applications such as gas leak localization, radiation monitoring, and environmental surveillance, where the origin of an unknown signal field must be estimated from spatial measurements. In practice, the source location is not directly observable and must be inferred from noisy scalar measurements collected during motion.In robotic source seeking, estimation and motion are closely linked: measurements improve the source estimate, while the chosen trajectory affects the quality of future measurements.Existing loop-based geometric strategies generate feasible motion but do not explicitly use estimation uncertainty to regulate direction updates.This paper presents a loop-based source-seeking framework that combines Extended Kalman Filter (EKF) estimation with Fisher Information Matrix (FIM)-based direction selection. The source estimate is updated during motion, and the heading is changed at loop boundaries using both estimation uncertainty and predicted information gain. A measurement-based stopping condition is used to detect convergence without requiring prior knowledge of the source location.Simulation results under stationary and moving source scenarios demonstrate improved tracking performance and reduced estimation error compared to purely information-driven or estimate-driven strategies.
Figures & tables
Fig. 1 : Planar source-seeking scenario. A sensor-mounted agent operates in a two-dimensional workspace and collects scalar field measurements generated by an unknown source.
Fig. 2 : Loop-based source-seeking strategy with direction updated at the end of each loop (switching point).
Fig. 3 : Trajectory comparison across three source dynamics (rows) and motion regulation strategies (columns). The information-driven dinfo(i) promotes exploration, while the estimate-driven dest(i) exploits the current source estimate. The joint strategy djoint(i) balances both, resulting in improved convergence, reduced tracking lag, and more stable trajectories across stationary and dynamic scenarios.
Fig. 4 : Estimation error ∥s^i,Ni−si,Ni∥ evaluated at switching points for stationary, non-maneuvering and maneuvering source source dynamics. The joint strategy achieves faster convergence and lower terminal error across all cases.
Fig. 5 : Distance to source ∥ri,Ni∥ versus loop index i for stationary, non-maneuvering and maneuvering source source dynamics. The joint strategy djoint(i) consistently yields faster convergence and reduced tracking lag compared to the information-driven dinfo(i) and estimate-driven dest(i) strategies.
Source Type
Turn-switching direction
d info (i)
d est (i)
d joint (i)
Stationary
1.569
0.457
0.366
Straight-line
1.507
2.033
0.265
Circular
4.761
2.946
1.010
TABLE I : Terminal estimation error (m) for different source types using turn-switching directions.
Informative path planning chooses robot routes and sensing actions that gather useful information while respecting travel, energy, time, and safety constraints.
{Closed-loop inverse source localization and characterization (ISLC) requires a mobile agent to select measurements that localize sources and infer latent field parameters under strict time constraints.} {The core challenge lies in the belief-space objective: valid uncertainty estimation requires expensive Bayesian inference, whereas using fast learned belief model leads to reward hacking, in which the policy exploits approximation errors rather than actually reducing uncertainty.} {We propose Distill-Belief, a teacher--student framework that decouples correctness from efficiency. A Bayes-correct particle-filter teacher maintains the posterior and supplies a dense information-gain signal, while a compact student distills the posterior into belief statistics for control and an uncertainty certificate for stopping. At deployment, only the student is used, yielding constant per-step cost.} {Experiments on seven field modalities and two stress tests show that Distill-Belief consistently reduces sensing cost and improves success, posterior contraction, and estimation accuracy over baselines, while mitigating reward hacking.}
Yiwei Shi, Zixing Song, Mengyue Yang +2
SEMT, University of Bristol, Bristol, UK · LUCAS, Loughborough University, Loughborough, UK
This paper presents a partial-scan-and-move strategy for source seeking with a mobile robot equipped with an offset scalar sensor. At each robot position, the sensor collects source field measurements while the robot rotates. Instead of requiring a complete circular scan before every move, we ask when the measurements collected over only part of the circle are already sufficient to determine the next action. We develop a gradient estimation method for partial scans together with a confidence set that accounts for measurement noise and local field variation. The robot uses this confidence set to decide whether it is close enough to the source or has enough information to move in a descent direction. We show that, under suitable conditions, each decision can be made within a prescribed partial scan and that the robot reaches a desired neighborhood of the source in finitely many moves with high probability.
Bo Wang, Ishvar Sitaldin
Department of Mechanical Engineering, The City College of New York, The City University of New York, New York, NY 10031, USA
Robotic localization under changing sensing conditions can suffer from biased errors and miscalibrated covariances. We present WRAP, an adapter-agnostic Wasserstein-robust plug-in for nonlinear extended Kalman filter (EKF) and error-state Kalman filter (ESKF) stacks. A causal module supplies time-varying effective process and measurement statistics; a mean-preserving Wasserstein local update then computes least-favorable covariances and a robust gain without changing the propagation model, residual, or retraction. This separates mean adaptation from covariance robustification and uses distinct radii for propagation and sensing. On 18 UWB--IMU sequences held out from adapter training, adapter-only and WRAP reduce mean 3-D position RMSE by 19.8% and 27.4% relative to the nominal ESKF; an isotropic ablation reaches 19.5%, linking the incremental gain to directional process-covariance redistribution. An in-sample GNSS--INS study shows that mean adaptation provides most of the accuracy gain, while DR improves consistency and mitigates over-tightened classical covariance estimates. The robust solve takes 0.05 ms for UWB and 2.92 ms for GNSS on a Jetson Orin Nano.
Minhyuk Jang, Astghik Hakobyan, Jungjin Lee +2
Department of Mechanical Science and Engineering, Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, IL, USA · Center for Scientific Innovation and Education and the National Polytechnic University of Armenia, Yerevan, Armenia · Department of Electrical and Computer Engineering and Automation and Systems Research Institute, Seoul National University, Seoul, South Korea