Oct 2026· IEEE Robotics and Automation Letters· Vol 11, pp. 11227-11234· 0 citations· 36 references
Abstract
Aerial robots equipped with cables used as soft end-effectors represent a new, versatile robotic paradigm to solve multiple tasks. However, to fully exploit the versatility of soft robots, the modeling problem must be addressed. The main challenges depend on the hard-to-model continuum dynamics. To solve this challenge, this work proposes multiple physics-informed neural network architectures to model a cable’s dynamics using Cartesian measurements. We apply a classic Lagrangian Neural Network architecture and propose a new Lagrangian-informed Transformer-based architecture, and establish local contraction bounds for their training dynamics. Furthermore, both networks address the underactuation of the system, highlight its mechanical nature, and return the cable positions, velocities, and accelerations in Cartesian space, enforcing energy conservation by exploiting the Lagrangian structure. Finally, we test the modeling performance via experiments with varying trajectories and models, comparing the proposed architectures with state-of-the-art networks and reduced-order model baselines.
The demand for robotic manipulators has increased because of their precision, speed, and cost-efficiency in complex or hazardous tasks. Flexible robotic manipulators, unlike rigid ones, offer lower mass and energy consumption, enabling advanced applications across various fields. Despite these advantages, the mass reduction of these manipulators can lead to undesired effects, including decreased precision, increased sensitivity to parametric uncertainties, coupled dynamics, and increased oscillations caused by their inherent flexibility. Moreover, the modeling complexity of such mechanical systems represents a significant challenge, since multiple degrees of freedom must be considered. In this study, a physics-informed neural network (PINN) is designed to estimate the dynamic behavior of a flexible-link manipulator. First, a dataset is created by executing different trajectories (i.e., different rotation angles) of the flexible manipulator. Based on the dataset, the PINN is then trained using time and strain signals as inputs to estimate the angular displacement, combining a data-driven loss with a physics-based loss derived from the system’s dynamic model. Finally, the PINN model is investigated experimentally to assess the closed-loop strategy and evaluate its efficiency and reproducibility in recognizing the mechanical system behavior. Therefore, the results show that the PINN and closed-loop experimental validations are consistent with the proposed method.
Tony Jun Tanaka, R. Geronel, R. Teloli et al.· Machines· 0 citations
Inverse kinematics (IK) is fundamental to robot motion planning. Classical analytical solvers require complete Denavit–Hartenberg (DH) parameters that are often proprietary or degraded by mechanical wear, and numerical solvers based on damped least squares (DLS) are sensitive to initialization, particularly near singularities. We propose XGNN, an explainable graph neural network positioned as a model-free, interpretable warm-start initializer for downstream numerical IK refinement rather than as a standalone replacement for analytical solvers. Each IK query is encoded as a 12-node graph in which six pose nodes and six joint nodes are connected through bipartite pose-to-joint attention edges and chain edges along the kinematic structure. GATv2 message passing aggregates information at each joint node; two ablation-validated design contributions (a learnable node-type embedding and an angle-aware composite loss) enable training to convergence. Evaluated on 300,000 trajectory-style samples generated from the ABB IRB 2400 kinematic model, XGNN achieves 3.66∘ joint mean absolute error (MAE), comparable to a multilayer perceptron baseline (3.09∘) and a bidirectional LSTM (3.14∘) under identical training. The standalone joint accuracy of all learned models is too coarse for direct industrial use, but XGNN provides the strongest warm start for DLS refinement: the convergence rate improves from 98.4% to 100%, mean iterations drop from 14.6 to 3.2, and wall-clock time per pose drops 5.0× on the IRB 2400. The benefit transfers cross-platform to the Universal Robots UR5 collaborative manipulator (convergence rate 82.2% to 100%, 10.0× speedup) and survives DH parameter perturbation of up to ±10%, simulating calibration drift or mechanical wear. The GATv2 attention coefficients additionally provide an interpretability signal at zero inference cost. XGNN therefore complements analytical and numerical IK methods as an interpretable, calibration-robust warm start when DH parameters are unavailable, proprietary, or degraded.
Ali Jlidi, Rabab Benotsmane, László Kovács· Electronics· 0 citations
Accurate modeling of deformable object dynamics is critical for robotic manipulation but remains challenging due to complex physics and strict physical constraints. In this paper, PhysCon-Deform is introduced, which is a mixed framework for specific tasks, combining residual neurodynamics learning and a differential augmented Lagrangian projection layer. Using a grid-based graph representation, PhysCon-Deform integrates a physics-based neurodynamics operator (PINDO) and a differentiable constraint projection module to achieve the deployment of residual correction, grid-based neurodynamics and model predictive control (MPC). Based on standard simulation benchmarks (Cloth3D, SoftGym and SoftMAC), our framework is always superior to the existing baselines in clean and disturbed environments. Specifically, it reduces long-term constraint violations by over 50%, demonstrates high robustness to end-effector trajectory noise, and enables efficient real-time trajectory optimization within an MPC pipeline. Extensive ablation and bias studies reveal that removing PINDO increases the prediction mean squared error (MSE) from 0.28 cm2 to 0.68 cm2 (a 143% increase), while omitting the constraint projection layer leads to a fourfold increase in violation rates. Furthermore, the robustness analysis of a colored noise and random walk drift model verifies its elasticity to non-ideal sensing. Although the deformation mechanism with a moderate rate-dependent effect in the simulation environment is optimized at present, PhysCon-Deform provides a very practical method to balance the precision-constraint trade-off in the control of deformable objects with physical constraints.
Forward kinematics is a fundamental component of robotic perception, planning, and control, yet it is commonly treated as a deterministic mapping that neglects variability arising from sensor noise, actuation imperfections, calibration errors, and unmodeled physical effects. Existing approaches to kinematic uncertainty estimation generally fall into three categories: analytical methods based on local linearization, which are computationally efficient but limited in capturing nonlinear and configuration-dependent effects; sampling-based techniques such as Monte Carlo simulation, which offer high accuracy at substantial computational cost; and learning-based methods that often assume homoscedastic uncertainty, thereby failing to represent the state-dependent variability observed in real robotic systems. This paper proposes a physics-informed framework for fast, configuration-dependent uncertainty quantification of robot forward kinematics using experimental data. A calibrated physics-based forward kinematics model is retained as a deterministic mean, while heteroscedastic uncertainty is learned as a configuration-dependent residual from real robot observations. The proposed approach is evaluated on a UR3 industrial manipulator and compared against homoscedastic baselines as well as representative learning-based uncertainty models, with additional sensitivity analyses used to assess robustness with respect to key architectural and training parameters. Experimental results demonstrate that the learned uncertainty consistently bounds the observed end-effector variability for both translational and rotational components, while achieving improved probabilistic calibration, reliable empirical coverage, and significantly lower inference cost. The method supports microsecond-level CPU inference, making it suitable for real-time uncertainty-aware robotic applications.
D. Nguyen, Xuân Thắng Vũ, Truong Do et al.· Journal of Mechanisms and Ro...· 1 citation
Forecasting the long-horizon evolution of mechanical systems from position-only observations is a pivotal yet difficult task, as hidden velocities and trajectory-specific physical properties must be inferred simultaneously. Although physics-guided neural networks like Lagrangian Neural Networks (LNNs) guarantee physical plausibility, they generally require complete state inputs and lack adaptability to changing system parameters. To break these limitations, we introduce History-informed Lagrangian Neural Networks (HiLNN). Grounded in the insight that temporal position sequences implicitly encode underlying dynamics, HiLNN employs a recurrent encoder to extract a latent context from history. This context not only reconstructs the unobserved initial velocity but also adaptively modulates the mass matrix, potential energy, and damping coefficients of a structured Lagrangian system. By leveraging a differentiable RK4 rollout scheme, the entire pipeline is optimized end-to-end under multi-step trajectory supervision and energy-consistency regularization. Empirical evaluations across conservative, dissipative, and heterogeneous variable-parameter systems show that HiLNN delivers superior long-term prediction accuracy and maintains precise energy profiles compared to state-of-the-art baselines. The source code is publicly available at https://github.com/yingtian22/History-informed-LNN.
Tianshuo Zhang, Xianglei Xing, Wenzhe Zhai et al.· 0 citations
This paper investigates the use of deep neural networks (DNNs) for solving inverse kinematics problems exhibiting multiple valid joint-space solutions. A synthetic dataset is generated from the forward kinematics of the ABB IRB120 manipulator, with end-effector orientation represented using unit quaternions, and a DNN is trained to approximate the relationship between Cartesian pose and joint configuration under three scenarios: (i) full joint space, (ii) constrained joint space with fixed $q_{6}$ , and (iii) a hybrid approach combining neural inference with nonlinear optimization. The results show that, in the full joint space, the inverse kinematics mapping is inherently multi-valued, preventing the DNN from learning a consistent and physically realizable inverse mapping through deterministic regression and leading to large prediction errors. In contrast, constraining $q_{6}$ reduces the ambiguity present in the training dataset and improves learning stability at the cost of restricting the solution space. The hybrid formulation mitigates these limitations by using the DNN to provide an informed initial estimate for a nonlinear least-squares solver operating in the full joint space. The proposed Hybrid-DNN formulation achieves a mean position error of 1.406 mm, a mean orientation error of 0.900°, and a success rate of 94.2%, where success is defined as simultaneously achieving position and orientation errors below 5 mm and 2°, respectively. Although slightly less accurate than the Conventional-Multistart-10 baseline, it achieves near-equivalent solution quality while reducing the average number of function evaluations and execution time by approximately 95.1% and 82.5%, respectively. These results indicate that inverse kinematics problems characterized by one-to-many mappings cannot be effectively treated as deterministic regression tasks and demonstrate that informed neural initialization combined with numerical optimization constitutes an effective and computationally efficient solution strategy.
Laércio Raimundo Filho, W. M. D. Santos· IEEE Access· 0 citations