In practical applications, robotic operating environments are typically open and dynamic, where robots frequently encounter previously unseen objects. Continual learning provides an effective solution for robotic object recognition by incrementally acquiring knowledge of novel objects while mitigating catastrophic forgetting. However, most continual learning methods assume that the labels of all the data are available, which is impractical in real-world scenarios—robots often encounter streams of unlabeled data with limited opportunities for expert annotation. This limitation raises two challenges: selecting the most valuable samples for labeling and effectively leveraging abundant unlabeled data to enhance learning. To address these challenges, we propose an Active Semi-supervised Continual Learning (ASCL) framework for robotic lifelong object recognition. The ASCL framework operates through three key mechanisms: (1) actively selecting the most representative and diverse samples for annotation using feature clustering and distance metrics, (2) generating reliable pseudo-labels for unlabeled data by exploiting feature-space neighborhood relationships and classifier confidence measures, and (3) implementing unlabeled task-key training combined with prompt tuning to enable effective semi-supervised continual learning. Experimental results show that ASCL achieves significant performance gains on real-world robotic datasets. Notably, even with limited labeled data, it attains near-fully-supervised performance levels, demonstrating strong continual learning capabilities in label-scarce scenarios.