Vision systems mounted on home robots need to interact with unseen classes in changing environments. Robots have limited computational resources, labelled data and storage capability. These requirements pose some unique challenges: models should adapt without forgetting past knowledge in a data- and parameter-efficient way. We characterize the problem as few-shot (FS) online continual learning (OCL), where robotic agents learn from a non-repeated stream of few-shot data updating only a few model parameters. Additionally, such models experience variable conditions at test time, where objects may appear in different poses (e.g., horizontal or vertical) and environments (e.g., day or night). To improve robustness of CL agents, we propose RobOCLe, which; 1) constructs an enriched feature space computing high order statistical moments from the embedded features of samples; and 2) computes similarity between high order statistics of the samples on the enriched feature space, and predicts their class labels. We evaluate robustness of CL models to train/test augmentations in various cases. We show that different moments allow RobOCLe to capture different properties of deformations, providing higher robustness with no decrease of inference speed.