Physics Informed Neural Network for feedforward control of a 2-DOF manipulator with flexure joints

Feedforward control of a manipulator can be generated with a sufficiently accurate stable inverse model of the manipulator. It has been demonstrated before that a Lagrangian Neural Network (LNN), or Deep Lagrangian Networks (DeLaN), can be trained to estimate the conservative part of the driving forces for a specified trajectory. Such network is bound to physical constraints and hence can predict the (inverse) multibody system behaviour quite accurately and robustly from a relatively small dataset. However, it does not account for non-conservative contributions to the forces.
To include damping and friction in the estimates, this paper proposes to include additional terms in the underlying equations to obtain a so-called DeLaN+D. The performance of this network is evaluated with simulated and experimental data from a fully actuated 2-DOF manipulator with flexure joints. The achievable accuracy of the predicted feedforward forces appears to be better than 97% in experiments with a validation trajectory. The tracking accuracy during controlled motion is improved with about 80% using feedforward control with this DeLaN+D, which is comparable to using identified inverse multibody system dynamics.