Probabilistic Latent Variable Modeling for Dynamic Friction Identification and Estimation

Precise identification of dynamic models in robotics is essential to support control design, friction compensation, output torque estimation, etc. A longstanding challenge remains in the identification of friction models for robotic joints, given the numerous physical phenomena affecting the underlying friction dynamics which result into nonlinear characteristics and hysteresis behaviour in particular. These phenomena proof difficult to be modelled and captured accurately using physical analogies alone. This has motivated researchers to shift from physics-based to data-driven models. Currently, these methods are still limited in their ability to generalize effectively to typical industrial robot deployement, characterized by high- and low-velocity operations and frequent direction reversals. Empirical observations motivate the use of dynamic friction models but these remain particulary challenging to establish. To address the current limitations, we propose to account for unidentified dynamics in the robot joints using latent dynamic states. The friction model may then utilize both the dynamic robot state and additional information encoded in the latent state to evaluate the friction torque. We cast this stochastic and partially unsupervised identification problem as a standard probabilistic representation learning problem. In this work both the friction model and latent state dynamics are parametrized as neural networks and integrated in the conventional lumped parameter dynamic robot model. The complete dynamics model is directly learned from the noisy encoder measurements in the robot joints. We use the Expectation-Maximisation (EM) algorithm to find a Maximum Likelihood Estimate (MLE) of the model parameters. The effectiveness of the proposed method is validated in terms of open-loop prediction accuracy in comparison with baseline methods, using the Kuka KR6 R700 as a test platform.