Hardness is one of the most critical tactile properties for robots to recognize objects. Machine learning methods have shown superior performance in object hardness classification. However, existing machine learning methods for tactile hardness classification cannot use the ordinal information between hardness classes because the one-hot encoding only cares about the correct class and ignores the inter-class relationship. To solve this problem, we propose to generalize the one-hot encoding using unimodal distributions including the Poisson and binomial distributions for tactile ordinal classification problems, resulting in two tactile ordinal networks (TacONet): TacONet-p and TacONet-b. Furthermore, we collect a tactile hardness dataset on the silicone samples with three different shapes (Shapes A, B, C), and each shape samples have thirteen hardness classes ranging from 0A (Shore A scale) to 60A at 5A intervals. We validate the resulting method for tactile hardness classification using a real robot. Experimental results demonstrate that compared with state-of-the-art methods, the proposed method achieves better classification performance in terms of accuracy and quadratic weighted kappa (QWK) on the tactile hardness dataset, reaching a classification accuracy up to 99.5% and a QWK up to 99.9% on Shape C. <i>Note to Practitioners</i>—In the field of robotics tactile recognition, hardness classification is one of the most important and common tasks for robots to accurately recognize objects, particularly when the environment is dark or visual sensors are not working. In this paper, we propose a novel tactile ordinal network for tactile hardness classification tasks. The existing machine learning models for tactile hardness classification are trained by minimizing the cross-entropy loss between predicted vectors and one-hot encoding vectors of true classes, which makes the models only care about the correct classes and ignores the inter-class relationship of hardness classes. In other words, these models have the same probability to misclassify a hardness class with any other hardness class. To tackle this problem, we propose to generalize the one-hot encoding method using a unimodal distribution method to encode the true classes. The unimodal distribution encoding vectors can make the model learn the ordinal information between classes. It is proved that the proposed method is able to effectively improve the classification accuracy and QWK in a tactile hardness classification task.
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