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

Summary

This paper investigates temporal neural networks for \mbox{end-effector} position \mbox{estimation} of an aerial continuum manipulator (ACM) operating under aerodynamic effects induced by the unmanned aerial vehicle (UAV).

Abstract Summary

Key Points

• This paper investigates temporal neural networks for \mbox{end-effector} position \mbox{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 (\mbox{rotor-off}) and \mbox{free-hovering} conditions across continuum robot (CR) configurations and UAV altitudes, providing \mbox{end-effector} position measurements with and without aerodynamic residuals.
• To establish a nominal framework, \mbox{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 \mbox{closed-form} \mbox{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.

Problem Formulation and Methodology

Let $s\in[0,L]$ denote the arc-length coordinate along a CR, where $L$ is its undeformed length. The configuration of a cross-section at $s$ relative to the base frame is represented by where $\bm{R}(s)\in\mathrm{SO}(3)$ and $\bm{r}(s)\in\mathbb{R}^{3}$ denote the cross-section orientation and position, respectively.

Experimental Setup and Dataset Generation

Fig. 1 shows the experimental platform used for dataset generation, consisting of a tendon-driven CR rigidly mounted on a UAV. The CR workspace is partitioned into 12 slices defined by prescribed ranges of $q_{1}$. For each experiment, $q_{1}$ is set to the midpoint of the corresponding range and held constant, while $q_{2}$ undergoes reciprocating motion.

Thus, $\dot{q}_{1}=0$ during each experiment and is not included as a model input.

Results

The nominal CR kinematics is identified from the baseline dataset in two steps. First, strain-parameterized models with constant through cubic spatial bases are compared using Test 17 ($q_{2}=0$), where deformation occurs predominantly in the principal bending plane. Measurements with similar $q_{1}$ values are averaged to approximate the nominal static relationship and reduce variability due to reciprocating motion.

Sources and Demonstrations

Figures are reproduced from Amiri et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.