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

Haoyu Sun; Meng Zhao; Tianhao Wang; Jianxu Wu

cs.ROApr 2, 2026

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

Authors: Haoyu Sun, Meng Zhao, Tianhao Wang, Jianxu Wu

Organizations: School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China.

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 & tables

Fig. 1 : D-H parameterization schematic of the Bennett mechanism.

Fig. 2 : 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.

Fig. 3 : 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.

Fig. 4 : 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. 3 .

Fig. 5 : 3D trajectory comparison of ablation configurations and baselines across randomly selected validation samples. Color coding follows Fig. 3 . Baselines without a trajectory-decoding branch (MLP-Direct, PointNet-Only) predict parameters directly and thus show no Pred curve (red dashed).

	Sub-group	Method	Params	Param-MAE $\downarrow$	$\mathbf{a_{12}}$ -MAE $\downarrow$	$\boldsymbol{\alpha_{12}}$ -MAE $\downarrow$	Traj-MAE $\downarrow$	Vel-MAE $\downarrow$
Proposed		O-ConNet (Full)	5.00M	$0.276{\pm}0.077$	$\mathbf{0.0063{\pm}0.0013}$	$\mathbf{0.316{\pm}0.063}$	$\mathbf{0.145{\pm}0.018}$	$\mathbf{0.017{\pm}0.002}$
Ablation	Enc. Pooling	MaxPool+AttnPool	5.13M	$\mathbf{0.260{\pm}0.084}$	$0.0065{\pm}0.0008$	$0.337{\pm}0.118$	$0.149{\pm}0.025$	$0.017{\pm}0.003$
		MaxPool only	4.97M	$0.283{\pm}0.109$	$0.0067{\pm}0.0010$	$0.339{\pm}0.131$	$0.175{\pm}0.031$	$0.018{\pm}0.003$
		MaxPool+AvgPool	5.10M	$0.286{\pm}0.114$	$0.0065{\pm}0.0012$	$0.336{\pm}0.122$	$0.154{\pm}0.033$	$0.018{\pm}0.004$
	Param. Head	w/o ResNet Residual	4.97M	$0.391{\pm}0.079$	$0.0088{\pm}0.0018$	$0.502{\pm}0.106$	$0.199{\pm}0.017$	$0.021{\pm}0.001$
	Param. Head	w/o Aux. Branch Loss	5.00M	$0.301{\pm}0.076$	$0.0056{\pm}0.0009$	$0.345{\pm}0.090$	$0.160{\pm}0.025$	$0.018{\pm}0.002$

TABLE I : Comprehensive performance summary on the validation set. MLP-Direct and PointNet-Only lack trajectory decoding branches ( † ); corresponding metrics are marked “–”. Each ablation alters only one factor while keeping all others consistent with the full model. All metrics are computed in the normalized coordinate system; lower is better. All values are mean

\pm

std over 10 independent runs.

Trajectory Reconstruction

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Flexible-body Modeling, Kinematic Identification, and Assembly Accuracy of Overconstrained Spatial Linkages

Overconstrained rational single-loop linkages are efficient, compact, and low-cost custom mechanisms, yet their deployment in industrial settings is limited. In simulations, rigid body formulations fail due to redundant constraints. This study presents a flexible multibody modeling framework based on the floating frame of reference formulation, and delivers an overall accuracy analysis of assembled linkages prototypes. The approach is validated against 3D-printed PLA prototypes of a Bennett four-bar mechanism, including variants with intentional joint-axis misalignment, which theoretically, from the rigid body point of view, cannot be assembled. A supplementary contribution is delivered in the form of a kinematic parameter identification methodology suited for this type of mechanism with ill-conditioned Jacobian. The experimental and simulation results are compared and reveal that these overconstrained mechanisms exhibit a self-assembling tendency -- structural compliance drives the assembly toward the ideal geometric configuration, distributing constraint stress throughout the structure. Additional qualitative demonstrations using cardboard tubes and bamboo sticks as link building blocks confirm that functional mechanisms can be realized from low-cost, unconventional materials with limited manufacturing accuracy. The proposed modeling pipeline is fully algorithmic and enables design optimization in the future.

Daniel Huczala, Michael Pieber, Johannes Gerstmayr +6

Department of Mechanical Engineering, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Eonyang-eup, Ulju-gun, Ulsan, 44919, South Korea · Department of Machine Parts and Mechanisms, VSB – Technical University of Ostrava, 17. listopadu 2172/15, Ostrava, 70800, Czech Republic · Department of Mechatronics, University of Innsbruck, Technikerstraße 13, Innsbruck, 6020, Austria +2

Mechanism Design Multibody Dynamics System Identification

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Sep 18, 2026

LOInK: Learned Optimal Inverse Kinematics via Structured Neural Surrogate Models

We introduce Learned Optimal Inverse Kinematics (LOInK), a method to generate approximately optimal solutions to an inverse kinematics problem. When trained on data consisting of sampled configurations and associated task variables and a given cost function, LOInK learns a bi-Lipschitz invertible mapping from configuration space to a decoupled task/latent space, and moreover, the latent space is structured so as to place cost-minimizing solutions at the origin. This enables efficient sampling of cost-minimizing solutions via a network-inversion algorithm based on operator splitting. We demonstrate the proposed approach on three problems: an illustrative three degree-of-freedom manipulator problem; a quadrupedal climbing robot for which LOInK can generate near-optimal solutions on average 31 times faster and up to 100 times faster than a constrained optimization approach; and a simulated soft actuator as a purely data-driven example, in which LOInK can explicitly generate high-quality solutions, unlike existing generative approaches that require diverse sampling and evaluation of candidate solutions.

Michael Somerfield, Damian Abood, Ruigang Wang +1

Australian Robotic Inspection and Asset Management (ARIAM) Hub, the Australian Centre for Robotics (ACFR), and the School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Australia

Inverse Kinematics Robot Kinematics Latent Space Optimization

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Jun 8, 2026

RAM: Reachability Across Morphologies

Many stages of the robotic lifecycle, from morphology synthesis to operation, rely fundamentally on the reachable workspace. However, current methods for approximating workspaces are slow, imprecise, or tied to a single morphology. We introduce Reachability Across Morphologies (RAM): a morphology-conditioned, implicit neural representation that acts as a fast, differentiable surrogate for pose reachability, generalising to unseen morphologies while inherently accounting for self-collisions. RAM is trained on a large-scale dataset of

3\cdot10^{10}

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Tim Walter, Xinyu Chen, Jonathan Külz +1

Department of Computer Engineering, Technical University Munich, Germany · German Electron Synchrotron, University of Hamburg, Germany

Reachability Analysis Implicit Neural Representations Robotic Optimization Robot Motion Planning Robot Kinematics

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Abstract

Trajectory Reconstruction

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