This paper investigates temporal neural networks for end-effector position estimation of an aerial continuum manipulator (ACM) operating under aerodynamic effects induced by the unmanned aerial vehicle (UAV).
An experimental dataset is collected under stationary (rotor-off) and free-hovering conditions across continuum robot (CR) configurations and UAV altitudes, providing end-effector position measurements with and without aerodynamic residuals.
To establish a nominal framework, strain-parameterized kinematic models with progressively richer strain bases are evaluated to balance model complexity and prediction accuracy.
The selected nominal model then serves as the baseline for 3D position residual estimation using a closed-form continuous-time (CfC) neural network, with a multilayer perceptron (MLP) and a gated recurrent unit (GRU) used for comparison.
On unseen test experiments, the CfC achieves an RMSE of \(22.00\pm1.70~\mathrm{mm}\) over five random seeds, compared with \(36.38\pm3.58~\mathrm{mm}\) for the MLP and \(27.72\pm2.92~\mathrm{mm}\) for the GRU, corresponding to reductions of \(39.52\%\) and \(20.62\%,\) respectively.
These results demonstrate the effectiveness of continuous-time learning for end-effector position estimation under aerodynamic disturbances relative to static and discrete-time learning methods.