Temporal Learning for End-Effector Position Estimation under Aerodynamic Disturbances in Aerial Continuum Manipulation

This paper investigates temporal neural networks for mboxend-effector position mboxestimation of an aerial continuum manipulator (ACM) operating under aerodynamic effects induced by the unmanned aerial vehicle (UAV). An experimental dataset is collected under stationary (mboxrotor-off) and mboxfree-hovering conditions across continuum robot (CR) configurations and UAV altitudes, providing mboxend-effector position measurements with and without aerodynamic residuals. To establish a nominal framework, mboxstrain-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 mboxclosed-form mboxcontinuous-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±1.70~mm) over five random seeds, compared with (36.38±3.58~mm) for the MLP and (27.72±2.92~mm) for the GRU, corresponding to reductions of (39.52%) and (20.62%), respectively. These results demonstrate the effectiveness of mboxcontinuous-time learning for mboxend-effector position estimation under aerodynamic disturbances relative to static and mboxdiscrete-time learning methods.