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.

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