Source-linked AI summary
Switched Turn-based Adaptive Source Seeking Strategy using Estimation and Information-driven Direction of Improvement
Shubhra Banerjee, Satadal Ghosh
TL;DR
Robotic source seeking must infer an unobservable source from noisy measurements while choosing motion that improves future localization. The paper combines EKF estimation with FIM-based direction selection in loop-based motion, and reports improved tracking and reduced estimation error in stationary and moving-source simulations.
Problem
Source seeking must estimate an unknown signal origin from noisy spatial measurements while steering an agent toward the source; existing geometric strategies do not explicitly use estimation uncertainty for direction updates.
Method
A loop-based framework updates the source estimate with an EKF and selects loop-boundary directions using the estimate, FIM-derived information gain, or an adaptive combination.
Results
The joint strategy achieves improved convergence, reduced tracking lag, more stable trajectories, lower terminal estimation error, and more effective distance reduction across stationary and dynamic scenarios.
Takeaways & Limitations
Adaptive weighting combines exploration from information gain with exploitation from source estimation while retaining loop-based motion and measurement-based convergence detection.
Abstract
from arXiv · showhide
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.
I. INTRODUCTION
Source seeking estimates an unknown signal origin from noisy spatial measurements while steering an agent toward the source. The paper combines feasible loop-based motion with EKF estimation and information-driven direction updates to balance exploration and exploitation.
- Problem context: Source seeking uses onboard sensor measurements at different locations to estimate an unknown signal origin and steer an unmanned agent toward the source region.Applications include locating deep regions, pollutants, and radiation sources.
- Related approaches: Existing approaches include control-theoretic, estimation-based, information-theoretic, and geometric strategies, each emphasizing different motion or uncertainty considerations.Control methods can require difficult-to-measure states or produce sharp turns, motivating simpler geometric patterns.
- Related approaches: Geometric loop strategies support exploration and progressively improved source-direction estimates, but zigzagging trajectories can be kinodynamically infeasible.The cited limitation specifically concerns zigzagging robot trajectories.
- Contribution: The proposed turn-switching strategy follows nominal circular loops and changes direction at selected loop locations using EKF estimates, FIM information gain, or an adaptive combination.The adaptive combination is intended to balance exploration and exploitation while preserving feasible circular-loop motion.
- Problem setting: The framework targets a planar workspace in which a sensor-mounted agent measures a smooth scalar field generated by a stationary or time-varying source.The field is modeled as symmetric and radially decreasing from its maximum at the source.
B. Agent Motion Model
The agent uses unicycle motion and gathers measurements along constant-curvature loops. Directions are updated at loop switching points, and iteration stops when switching-point signal measurements no longer improve.
- Agent and measurements: The agent follows unicycle kinematics with positive forward speed and a controllable turn rate while collecting scalar measurements.Its state includes planar position and heading angle.
- Motion objective: The objective is kinodynamically feasible motion toward a small neighborhood of the source using estimated location and information-gain direction.The motion regulator uses the current estimate, associated uncertainty, and a Fisher Information Matrix-derived measure.
- Loop-based strategy: The strategy executes a sequence of constant-curvature loops and accumulates measurements within each loop to compute the next reference direction.Loop accumulation attenuates high-frequency noise and provides directional information for subsequent motion.
- Initial loop: At the initial loop, the agent explores without prior direction, terminates at the maximum measured signal, and computes a direction for the next loop.Subsequent directions use estimate-based, Fisher-information-based, or joint strategies.
- Subsequent loops: Subsequent loops terminate when the trajectory intersects a ray from the previous switching point along the previous direction, after which a new direction is estimated.The agent then changes motion direction and increments the loop counter.
- Stopping criterion: The process stops when measured signal at switching points ceases to improve across successive loops, indicating convergence near the source.This stopping rule uses measurements rather than prior knowledge of the source location.
B. Estimation-Based Direction
The estimation-based direction uses an EKF source estimate and covariance updated during each loop. At switching points, the agent steers according to the relative geometry between its position and the estimated source.
- EKF estimation: The source evolution and measurement models are evaluated at each discrete measurement step during loop-based motion.The estimate is used to determine subsequent loop termination and motion switching.
- EKF estimation: The EKF maintains a source-location estimate and associated covariance at each measurement step within a loop.It applies prediction and update steps for the nonlinear source and measurement models.
- EKF estimation: The EKF uses Jacobians of the source evolution and measurement functions, with the Kalman gain and agent position entering the update computation.The measurement Jacobian is evaluated using the agent position and predicted source state.
- Estimate-based direction: The estimate-based direction is defined at a switching point from the relative geometry between the agent and the estimated source location.The direction is denoted d(i)_est and is derived from the EKF source estimate.
Results:
The estimate-based direction improves monotonically across loops, and its direction error decreases exponentially under standard EKF assumptions.
- The estimate-based direction improves monotonically across loops as EKF estimation improves.
- The true source direction is defined at each loop’s switching point for evaluating direction error.
- Nonzero measurement information makes the loop-wise improvement strict.
- The convergence bound assumes a nonzero source-relative vector norm and incorporates initial estimation error and noise statistics.
- The direction error decreases monotonically and exhibits exponential convergence under standard EKF assumptions.
C. Fisher Information-Based Direction
The information-driven strategy regulates motion to maximize information gained about the source location.
- The information-driven strategy regulates agent motion to maximize information gained about the source location.
Fisher Information and Direction Definition:
The method accumulates Fisher information from measurement Jacobians and selects a normalized direction along the spatial gradient of its trace.
- At each measurement step, the Fisher Information Matrix is formed from the measurement Jacobian evaluated at the agent position and source estimate.
- Information is accumulated over the loop as a sum of measurement-information contributions.
- The information-based direction is the normalized gradient of the accumulated FIM trace at the switching point.
- The gradient is evaluated numerically using the source estimate at the switching point.
D. Direction Estimation Using Joint Strategy
The joint strategy combines estimate-based and information-based directions to balance exploitation and exploration, with adaptive weighting tied to estimation uncertainty.
- The joint direction combines information-based and estimate-based directions to balance exploration and exploitation.
- When estimation uncertainty is large, adaptive weighting prioritizes information gathering; as accuracy improves, motion aligns increasingly with the estimate.
- The joint direction yields strictly smaller expected direction error than the estimate-based direction.
- The joint direction achieves strictly greater information gain than the estimate-only strategy because it includes a nonzero information-driven component.
E. Convergence
The convergence analysis shows that loop-based motion progressively reduces source distance, while the joint strategy improves directional alignment and progression compared with estimate-only and information-only strategies.
- The proposed loop-based motion progressively reduces the distance to the source across successive switching points.
- The estimate-based strategy ensures monotonic distance reduction and eventual convergence to the source.
- The joint strategy achieves smaller direction error than the estimate-based direction, improving alignment with the true source direction.
- The joint strategy yields greater distance reduction per loop and faster progression than estimate-only and information-only strategies.
IV. SIMULATION RESULTS
Simulations evaluate three turn-switching directions across stationary, straight-line, and circular source motions. The joint strategy combines estimated-source and information-driven directions to balance exploration and exploitation, while information-only motion can oscillate after information saturates.
- Simulations use a Gaussian scalar field with stationary, straight-line, and circular source motions.The moving-source cases use 0.10 m/s source velocity; circular motion has angular rate 0.01 rad/s and radius 10 m.
- Three turn-switching directions are evaluated: FIM-only, estimate-only, and a joint adaptive combination.The joint direction uses adaptive weight λ_i to balance exploration and exploitation.
- The joint strategy initially steers toward the source in both stationary and dynamic scenarios.
- After information saturates, the information-only direction oscillates with large deviation and performs poorly in final convergence.
- In dynamic scenarios, the joint strategy continues exploring and exploiting later in the mission, improving convergence to the moving source’s closer proximity.
B. Estimation Error Evolution
Across stationary and dynamic source scenarios, the joint strategy achieves the lowest terminal estimation error, outperforming information-only and estimate-only directions.
- The joint strategy achieves the lowest terminal estimation error across all source dynamics.
- 0.366 m is the stationary-case error for the joint strategy, compared with 1.569 m for information-only and 0.457 m for estimate-only.
- 1.01 m is the circular-motion error for the joint strategy, while the information-only and estimate-only strategies have higher residual errors.
C. Distance-to-Source Evolution
The joint strategy reduces agent–source distance faster and approaches a closer neighborhood across stationary and dynamic scenarios. Its loop-based formulation supports smooth, curvature-bounded motion while combining exploration with exploitation.
- The joint strategy shows consistently faster reduction in agent–source Euclidean distance across all source dynamics.
- The information-only strategy suffers at the end of convergence, whereas the joint and estimate-based strategies reach a sufficiently small neighborhood around the source.
- Across stationary and dynamic scenarios, the joint strategy converges faster and approaches the source more closely.
- The joint direction balances information-driven exploration with estimate-driven exploitation through adaptive weighting.
- Loop-based direction updates use aggregated information rather than noisy instantaneous data, producing smooth, curvature-bounded motion.
- The framework is supported by simulations for stationary and moving sources, with future work extending it to 3D scenarios and real-world experiments.