While collaborative perception (CP) enhances the safety of autonomous driving, limited bandwidth can cause severe shared data staleness in CP systems. Existing age-of-information (AoI) minimization policies are not well-suited for CP, as they overlook the fact that a vehicle's AoI decreases not only through updates from the source (i.e., a base station) but also through the vehicle's local sensing. To address this issue, we propose a mobility-aware AoI minimization framework for CP that explicitly accounts for vehicles' dynamic sensing ranges. We first derive a closed-form expression for the long-term time average sum AoI within a considered region, accommodating an ever-changing vehicle population and their dynamic sensed areas. Based on this characterization, we develop Local-sensing-aware Max-Weight Scheduling (LocMW), an online learning algorithm designed for sensor information broadcast from a source to vehicles under unknown environmental statistics and delayed observations. We provide performance guarantees demonstrating that LocMW achieves a sublinear cumulative excess AoI compared to the optimal stationary randomized benchmark. Extensive simulations using vehicular trajectory datasets and 3D perception tasks demonstrate that our LocMW policy substantially outperforms competing baselines, reducing the time-averaged sum AoI by up to 31.6% and improving mAP detection accuracy by up to 16.3%.

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