In several mechanical applications, the knowledge of the external inputs is of paramount importance during the operational phase, for instance for durability or energy assessments. However, while acceleration or position sensors are relatively common and inexpensive, force and torque sensors may be unfeasible to mount in practice for economic or geometric reasons. In this case, the (available) system model can be combined with the (available) sensors in an estimation scheme in order to indirectly assess the unknown inputs.In the case of complex mechanisms, multibody models are typically employed. They usually describe the system with a set of redundant variables related by constraints which leads to differential algebraic equations. This equations of motion structure cannot be directly combined with common estimation schemes as they usually deal with ordinary differential equations.In this work, a deep learning framework is proposed in order to reduce a generic rigid multibody model to independent coordinates and obtain its state-space formulation. The known multibody dynamics is combined with the neural network in order to promote its generalization and the (offline) training phase dataset can be based on a purely numerical simulation dataset, without requiring knowledge of the constraint equations or dedicated solution schemes.The obtained ordinary-differential-equation model is then ready to be embedded in a (discrete) extended augmented Kalman &nbsp;filter. In this operational phase, the sensor measures are employed for the concurrent estimation of states and inputs.An experimental validation on a SCARA robot is conduced. The mapping between the original full multibody coordinates and the two (angular) minimal coordinates is learnt with a neural network based on numerical data. Then, the measured system states, i.e. the two arm angles and velocities, are employed to estimate the two (supposedly unknown) motor torques. The comparison with the real torque values shows a good accuracy.In general, the procedure is applicable on a mechanisms with multiple independent coordinates, spatial mechanisms with closed loops (for which analytical independent coordinates cannot be obtained) and acceleration-level measure can be sufficient to obtain an observable system and a stable estimation. It is therefore a promising approach for a general, non-invasive implementation of multibody models in estimation or control schemes.

A Kalman Filter for State-Input Estimation With Rigid Multibody Models Based on the Deep Learning of Minimal Coordinates

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

ASME 2021 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE2021)

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