The ability to recognize the surface type is crucial for both indoor and outdoor mobile robots. Knowing the surface type can help indoor mobile robots move more safely and adjust their movement accordingly. However, recognizing surface characteristics is challenging since similar planes can appear substantially different; for instance, carpets come in various types and colors. To address this inherent uncertainty in vision-based surface classification, this study first generates a new, unique data set composed of 2,081 surface images (carpet, tiles, and wood) captured in different indoor environments. Secondly, the pre-trained state-of-the-art deep learning models, namely InceptionV3, VGG16, VGG19, ResNet50, Xception, InceptionResNetV2, and MobileNetV2, were utilized to recognize the surface type. Additionally, a lightweight MobileNetV2-modified model was proposed for surface classification. The proposed model has approximately four times fewer total parameters than the original MobileNetV2 model, reducing the size of the trained model weights from 42 MB to 11 MB. Thus, the proposed model can be used in robotic systems with limited computational capacity and embedded systems. Lastly, several optimizers, such as SGD, RMSProp, Adam, Adadelta, Adamax, Adagrad, and Nadam, are applied to distinguish the most efficient network. Experimental results demonstrate that the proposed model outperforms all other applied methods and existing approaches in the literature by achieving 99.52% accuracy and an average score of 99.66% in precision, recall, and F1-score. In addition to this, the proposed lightweight model was tested in real-time on a mobile robot in 11 scenarios consisting of various indoor environments such as offices, hallways, and homes, resulting in an accuracy of 99.25%. Finally, each model was evaluated in terms of model loading time and processing time. The proposed model requires less loading and processing time than the other models.