Out of Distribution Detection via Domain-Informed Gaussian Process State Space Models

In order for robots to safely navigate in unseen scenarios using learning-based methods, it is important to accurately detect out-of-training-distribution (OoD) situations online. Recently, Gaussian process state-space models (GPSSMs) have proven useful to discriminate unexpected observations by comparing them against probabilistic predictions. However, the capability for the model to correctly distinguish between in- and out-of-training distribution observations hinges on the accuracy of these predictions, primarily affected by the class of functions the GPSSM kernel can represent. In this paper, we propose (i) a novel approach to embed existing domain knowledge in the kernel and (ii) an OoD online runtime monitor, based on receding-horizon predictions. Domain knowledge is provided in the form of a dataset, collected either in simulation or by using a nominal model. Numerical results show that the informed kernel yields better regression quality with smaller datasets, as compared to standard kernel choices. We demonstrate the effectiveness of the OoD monitor on a real quadruped navigating an indoor setting, which reliably classifies previously unseen terrains.