In order for robots to safely navigate in unseen scenarios, it is desirable to rely on algorithms capable of efficiently detecting out-of-training-distribution (OoD) situations online and with accuracy. 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 discriminate hinges on the accuracy of these predictions, which are primarily affected by the choice of the GP kernel, which restrains the family of functions the model can represent. In [1], we propose a novel approach to construct an informed kernel for the GPSSM using existing domain knowledge. The resulting kernel is non-stationary and the construction procedure only requires access to a (potentially) incorrect nominal model or a simulator. Numerical results show that this kernel outperforms standard kernel choices. We use this method to detect OoD situations on a real quadruped navigating an indoors setting with changing terrains. This is illustrated in Fig. 1, where a quadruped learns its dynamical model by walking in circles (first column) and then it is exposed to two different environments, rope-pulling (second column) and rocky terrain (third column). The proposed metric captures the moments in which the robot is most likely to be OoD by comparing long-term model predictions with observations.

References

[1] Out of Distribution Detection via Domain-Informed Gaussian Process State Space Models
A. Marco, Elias Morley, Claire J. Tomlin Proceedings of the 56th IEEE Annual Conference on Decision and Control (CDC), Dec. 2023 (to appear)