Long-term autonomy requires robust navigation in environments subject to dynamic and static changes, as well as adverse weather conditions. Teach-and-Repeat (T&R) navigation offers a reliable and cost-effective solution by avoiding the need for consistent global mapping; however, existing T&R systems lack a systematic solution to tackle various environmental variations such as weather degradation, ephemeral dynamics, and structural changes. This work proposes LTR$^{2}$, the first cross-modal, cross-platform LiDAR-Teach-and-Radar-Repeat system that systematically addresses these challenges. LTR$^{2}$leverages LiDAR during the teaching phase to capture precise structural information under normal conditions and utilizes 4D millimeter-wave radar during the repeating phase for robust operation under environmental degradations. To align sparse and noisy forward-looking 4D radar with dense and accurate omnidirectional 3D LiDAR data, we introduce a Cross-Modal Registration (CMR) network that jointly exploits Doppler-based motion priors and the physical laws governing LiDAR intensity and radar power density. Furthermore, we propose an adaptive fine-tuning strategy that incrementally updates the CMR network based on localization errors, enabling long-term adaptability to static environmental changes without ground-truth labels. We demonstrate that the proposed CMR network achieves state-of-the-art cross-modal registration performance on the open-access dataset. Then we validate LTR$^{2}$across three robot platforms over a large-scale, long-term deployment (40+ km over 6 months), including challenging conditions such as nighttime smoke. Experimental results and ablation studies demonstrate centimeter-level accuracy and strong robustness against diverse environmental disturbances, significantly outperforming existing approaches.

Multimodal sensor fusion has been successfully utilized in many odometry and localization methods as it increases both estimate accuracy and robustness in application scenarios. To address the challenge of odometry under varying-weather conditions, we propose a novel visual 4D radar fusion based odometry in an unsupervised deep learning approach. In our method, we adopt transformer-based cascaded decoders to facilitate efficient feature extraction of images and radar point clouds. Considering that radars are weather-agnostic and information-rich cameras are susceptible to adverse weathers, we deliberately introduce an adaptive attention-based feature fusion mechanism, in which the attention shifts dynamically to adapt to changing weather conditions based on the amount of information content in image features. Through extensive comparative experiments, our method surpasses different state-of-the-art single-modal odometry estimation methods. Our code and trained model will be released publicly.