O-ConNet: Geometry-Aware End-to-End Inference of Over-Constrained Spatial Mechanisms

Abstract

Deep learning has shown strong potential for scientific discovery, but its ability to model macroscopic rigid-body kinematic constraints remains underexplored. We study this problem on spatial over-constrained mechanisms and propose O-ConNet, an end-to-end framework that infers mechanism structural parameters from only three sparse reachable points while reconstructing the full motion trajectory, without explicitly solving constraint equations during inference. On a self-constructed Bennett 4R dataset of 42,860 valid samples, O-ConNet achieves Param-MAE 0.276 +/- 0.077 and Traj-MAE 0.145 +/- 0.018 (mean +/- std over 10 runs), outperforming the strongest sequence baseline (LSTM-Seq2Seq) by 65.1 percent and 88.2 percent, respectively. These results suggest that end-to-end learning can capture closed-loop geometric structure and provide a practical route for inverse design of spatial over-constrained mechanisms under extremely sparse observations.

Figures (5)

• Figure C1: D-H parameterization schematic of the Bennett mechanism.
• Figure C2: 3D trajectory visualization of dataset samples. Each panel displays the complete motion trajectory of a Bennett mechanism's third joint endpoint, with speed magnitude encoded by a plasma colormap.
• Figure D1: Complete architecture of O-ConNet. On the left, a permutation-invariant kinematic state encoder processes 3 sparse observation points through a shared-weight MLP and learnable attention pooling (AttnPool), compressing them into a global latent vector $\mathbf{z}\in\mathbb{R}^{512}$. In the center, a Transformer decoder expands $\mathbf{z}$ into 64-point trajectory coordinates $\hat{\mathbf{T}}$ and a velocity field $\hat{\mathbf{V}}$. On the right, the parameter prediction head adopts a ResNet-style shortcut-residual dual-path structure, where the shortcut branch maps $\mathbf{z}$ directly to coarse logits $\mathbf{s}$ (supervised by $\mathcal{L}_{\mathrm{aux}}$) and the residual branch reads the reconstructed trajectory to produce a zero-initialized refinement $\mathbf{r}$; the merged output is decoded via Sigmoid and atan2 into $(\hat{a}_{12},\hat{\alpha}_{12})$. In all trajectory visualizations throughout this paper, blue solid lines denote ground truth (GT), red dashed lines show the network prediction (Pred), green dotted lines represent the forward kinematic reconstruction from predicted parameters (Kin), and orange stars mark the input observation points.
• Figure E1: Trajectory prediction and kinematic verification comparison for three representative validation samples. Each row shows one sample; from left to right: 3D view and XY/XZ/YZ projections. Color coding follows Fig. \ref{['fig:network']}.
• Figure E2: 3D trajectory comparison of ablation configurations and baselines across randomly selected validation samples. Color coding follows Fig. \ref{['fig:network']}. Baselines without a trajectory-decoding branch (MLP-Direct, PointNet-Only) predict parameters directly and thus show no Pred curve (red dashed).