Rover-mounted robotic arms can extend human reach during lunar sample handling, but continuous joystick teleoperation requires repeated visual-motor alignment while operators may also need to monitor system states. This paper presents a gaze-assisted supervisory control framework in which gaze nominates a rock or placement target, explicit confirmation authorizes the action, and the robot performs bounded autonomous grasp-and-place execution. The framework was evaluated against manual joystick teleoperation in a mission-analog virtual reality study with 16 participants. The study used a 2 x 2 x 3 within-subject design varying control mode, placement difficulty, and concurrent monitoring load. Mean recorded task completion time decreased from 47.65 to 18.43 s per rock, with 72.5% of this difference arising during grasping. Under the tested auditory monitoring conditions, gaze-assisted supervisory control showed less average proportional slowing, with no detected control-mode difference in monitoring-response accuracy or speed. The rate of gaze shifts between core areas of interest decreased from 49.98 to 27.73 shifts/min, while the raw NASA Task Load Index score decreased from 32.54 to 18.26. However, the benefit was task dependent. In precision placement, manual control yielded lower mean placement error and a higher placement success rate. These findings support a mixed-initiative allocation in which gaze enables rapid task-level intention specification and autonomous execution, while precision-critical stages retain manual refinement.

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