Shape control of deformable linear objects (DLOs) is a major challenge in robotics due to their high-dimensional, nonlinear dynamics and sensitivity to boundary conditions. Existing data-driven and physics-based models either require large datasets or suffer from excessive computational cost for real-time control. This paper presents a Cosserat-based Physics-Informed Neural Network (C-PINN) framework for efficient, real-time DLO modeling and automatic shape control. By embedding Cosserat rod theory directly into the PINN loss, C-PINN achieves accurate, physically consistent predictions of the DLO while dramatically reducing the requirement for large-scale training data and is robust to unseen scenarios. To enhance generalization and training stability, we introduce a curriculum learning strategy and propose an online sim-to-real residual adaptation module to bridge the gap between simulation and real-world deployment. The learned surrogate model is integrated into a gradient-based model predictive controller (MPC), enabling real-time, closed-loop shape control. Extensive experiments demonstrate that our approach generalizes well to various DLO materials and configurations in both 2D and 3D scenarios, and adapts robustly to interactive, human-in-the-loop manipulation. Both simulation and real-world experiments show that our method consistently attains significantly lower RMSE, as confirmed by comprehensive comparisons with various baselines. These results highlight the effectiveness and versatility of C-PINN for practical, high-precision DLO manipulation in diverse robotic scenarios. Compared to traditional analytical solvers, C-PINN achieves up to a 228-fold improvement in computational speed.

Fast simulation of elastic bodies is fundamental to computer graphics, yet current leading methods have a key limitation: they require fixed mesh connectivity. Existing methods leverage this assumption to achieve high performance but fail during topological changes such as cutting, fracturing, or merging. We present CAN, a novel optimizer that fundamentally decouples simulation acceleration from mesh topology. CAN introduces two Hessian-free, curvature-aware components: a Curvature-Aware Momentum (CAM) scheme that prevents overshooting by adaptively decaying momentum based on local gradient variations, and a Curvature-Aware Line Search (CALS) that provides high-quality step sizes via efficient directional curvature approximations. Since CAN relies solely on per-vertex, historical information, it is inherently parallel and topology-agnostic. We demonstrate that CAN achieves superior convergence compared to prior works across a wide range of dynamic-topology scenarios without any precomputation tied to connectivity, establishing a new paradigm for robust and efficient physics-based animation.

Continuum robots offer high flexibility and multiple degrees of freedom, making them ideal for navigating narrow lumens. However, accurately modeling their behavior under large deformations and frequent environmental contacts remains challenging. Current methods for solving the deformation of these robots, such as the Model Order Reduction and Gauss-Seidel (GS) methods, suffer from significant drawbacks. They experience reduced computational speed as the number of contact points increases and struggle to balance speed with model accuracy. To overcome these limitations, we introduce a novel finite element method (FEM) named Acc-FEM. Acc-FEM employs a large deformation quasi-static finite element model and integrates an accelerated solver scheme to handle multi-contact simulations efficiently. Additionally, it utilizes parallel computing with Graphics Processing Units (GPU) for real-time updates of the finite element models and collision detection. Extensive numerical experiments demonstrate that Acc-Fem significantly improves computational efficiency in modeling continuum robots with multiple contacts while achieving satisfactory accuracy, addressing the deficiencies of existing methods.

We present a GPU-friendly framework for real-time implicit simulation of elastic material in the presence of frictional contacts. The integration of hyperelasticity, non-interpenetration contact, and friction in real-time simulations presents formidable nonlinear and non-smooth problems, which are highly challenging to solve. By incorporating nonlinear complementarity conditions within the local-global framework, we achieve rapid convergence in addressing these challenges. While the structure of local-global methods is not fully GPU-friendly, our proposal of a simple yet efficient solver with sparse presentation of the system inverse enables highly parallel computing while maintaining a fast convergence rate. Moreover, our novel splitting strategy for non-smooth indicators not only amplifies overall performance but also refines the complementarity preconditioner, enhancing the accuracy of frictional behavior modeling. Through extensive experimentation, the robustness of our framework in managing real-time contact scenarios, ranging from large-scale systems and extreme deformations to non-smooth contacts and precise friction interactions, has been validated. Compatible with a wide range of hyperelastic models, our approach maintains efficiency across both low and high stiffness materials. Despite its remarkable efficiency, robustness, and generality, our method is elegantly simple, with its core contributions grounded solely on standard matrix operations.

In this paper, we propose a strategy for the control of soft robots with visual tracking and simulation-based predictor. A kinematic model of soft robots is obtained thanks to the Finite Element Method (FEM) computed in real-time. The FEM allows to obtain a prediction of the Jacobian matrix of the robot. This allows a first control of the robot, in the actuator space. Then, a second control strategy based on the feedback of infrared cameras is developed to obtain a correction of the effector position. The robust stability of this closed-loop system is obtained based on Lyapunov stability theory. Otherwise, to deal with the problem of image features (the marker points placed on the end effector of soft robot) loss, a switched control strategy is proposed to combine both the open-loop controller and the closed-loop controller. Finally, experiments on a parallel soft robot driven by four cables are conducted and show the effectiveness of these methods for the real-time control of soft robots.

This paper aims at providing a novel approach to modeling and controlling soft robots. Based on real-time Finite Element Method (FEM), we obtain a globally defined discrete-time kinematic model in the workspace of soft robots. From the kinematic equations, we deduce the soft-robot Jacobian matrix and discuss the conditions to avoid singular configurations. Then, we propose a novel observer based control methodology where the observer is built by Finite Element Model in this paper to deal with the control problem of soft robots. A closed-loop controller for position control of soft robot is designed based on the discrete-time model with feedback signal being extracted by means of visual servoing. Finally, experimental results on a parallel soft robot show the efficiency and performance of our proposed controller.