Precise identification of dynamic models in robotics is essential to support dynamic simulations, control design, friction compensation, output torque estimation, etc. A longstanding challenge remains in the development and 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 are 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.

There is an emerging industrial demand for predictive maintenance algorithms that exhibit high levels of predictive accuracy. Such condition monitoring tools must estimate dynamic quantities, such as Remaining Useful Lifetime (RUL) and the State of Health (SOH), based on a, typically, restricted set of measurements that can be obtained in an operational setting. These quantities exhibit inherent stochasticity and can only be approximately determined a posteriori to system failure. This paper proposes a generic prognostic tool for probabilistic condition monitoring of mechatronic systems, with the aim to improve the probabilistic prediction of condition metrics, specifically RUL and SOH. Therefore we propose to identify a Hidden Markov Model (HMM) from a fully instrumented measurement set, that is only available for a restricted set of run-to-failure experiments, typically gathered in an R&D setting. Although being artificial and retrospectively constructed metrics, we interpret RUL and SOH as physical measurements with the purpose to identify accurate degradation dynamics. Once the degradation model is identified, we practice the mathematical flexibility of the HMM framework to estimate several of the no longer available dynamic quantities of interest in real-time, from the limited set of measurements that are available in an operational setting. This modelling paradigm is known as virtual sensing. Predictive performance and computational efficiency are further improved by domain knowledge based pre-processing of the measurements. We apply our methodology to solenoid valves (SV), a widely used and often critical component in many industrial systems, which display a large variation in useful lifetime. Benchmark results show that the predictive capabilities of the presented methodology compares with prognostic techniques that are more computationally and memory demanding.Note to Practitioners—The motivation for this research is twofold. First there is a pending industrial need for improved diagnostic and prognostic tools. Second there is the observation that lifetime tests usually take place in an R&D setting and that expert labelling of Remaining Useful Lifetime (RUL) or State of Health (SOH) of a component or system is often based on measurement data that is not available in the industrial setting where the prognostic tools are to be deployed in the end. These two observations suggest that there is large potential in methods that can correlate the expert labelling, in particular RUL & SOH signals, with measurement data that is available in the industrial setting. Our approach has been tested in detail on the case of Solenoid Valves, which are widely used in industry and that are often safety critical. Our experiments demonstrate that the method compares with brute force approaches that overpower ours both in terms of computational as well as memory requirements. The method is furthermore generic and there is no reason to assume it would not work for other applications.