Open-vocabulary object detection (OVD) lets robots search for run-time object queries, but fixed-rate inference spends embedded compute on low-value frames during idle motion, map revisits, or stable viewpoints. This paper presents an energy-aware OVD scheduler for low-power mobile robots. The scheduler uses odometry, map change, and detector confidence to switch among low-, mid-, and high-power YOLO-World-S modes on a Jetson Orin Nano. We evaluate the energy-quality trade-off on an AgileX LIMO using 40 real navigation trials: two target objects, five placements per target-policy pair, and four perception policies. Across bottle and cup trials, the scheduler records 8/10 mission success compared with 7/10 for each fixed-rate baseline, while reducing mean Jetson input power (a Jetson-side power-draw metric) by 5.2% relative to an 8 Hz high-rate baseline and lowering achieved OVD call rate by 34.0%. It does not minimize mission-window Jetson input energy because longer missions can erase instantaneous power savings. A separate 60 s stationary microbenchmark isolates the perception workload: the scheduler lowers mean power from 8.045 W to 7.301 W and energy from 484.7 J to 438.1 J relative to the 8 Hz baseline. These results support robot-state-aware OVD scheduling as a promising power-management mechanism with competitive task reliability, while showing that mission-window Jetson input energy must be read together with task progress and runtime.

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