Azad Artinian | Searcharxiv

arXiv2026

Constraint-Free Static Modeling of Continuum Parallel Robot

Continuum parallel robots (CPR) combine rigid actuation mechanisms with multiple elastic rods in a closed-loop topology, making forward statics challenging when rigid--continuum junctions are enforced by explicit kinematic constraints. Such constraint-based formulations typically introduce additional algebraic variables and complicate both numerical solution and downstream control. This paper presents a geometric exact, configuration-based and constraint-free static model of CPR that remains valid under geometrically nonlinear, large-deformation and large-rotation conditions. Connectivity constraints are eliminated by kinematic embedding, yielding a reduced unconstrained problem. Each rod of CPR is discretized by nodal poses on SE(3), while the element-wise strain field is reconstructed through a linear strain parameterization. A fourth-order Magnus approximation yields an explicit and geometrically consistent mapping between element end poses and the strain. Rigid attachments at the motor-driven base and the end-effector platforms are handled through kinematic embeddings. Based on total potential energy and virtual work, we derive assembly-ready residuals and explicit Newton tangents, and solve the resulting nonlinear equilibrium equations using a Riemannian Newton iteration on the product manifold. Experiments on a three-servomotor, six-rod prototype validate the model by showing good agreement between simulation and measurements for both unloaded motions and externally loaded cases.

cs.RO↗

arXiv2024

Closed-loop shape control of deformable linear objects based on Cosserat model

The robotic shape control of deformable linear objects has garnered increasing interest within the robotics community. Despite recent progress, the majority of shape control approaches can be classified into two main groups: open-loop control, which relies on physically realistic models to represent the object, and closed-loop control, which employs less precise models alongside visual data to compute commands. In this work, we present a novel 3D shape control approach that includes the physically realistic Cosserat model into a closed-loop control framework, using vision feedback to rectify errors in real-time. This approach capitalizes on the advantages of both groups: the realism and precision provided by physics-based models, and the rapid computation, therefore enabling real-time correction of model errors, and robustness to elastic parameter estimation inherent in vision-based approaches. This is achieved by computing a deformation Jacobian derived from both the Cosserat model and visual data. To demonstrate the effectiveness of the method, we conduct a series of shape control experiments where robots are tasked with deforming linear objects towards a desired shape.

cs.RO↗

arXiv2024

Optimal Cosserat-based deformation control for robotic manipulation of linear objects

The robotic shape control of deformable linear objects has garnered increasing interest within the robotics community. Despite recent progress, the majority of shape control approaches can be classified into two main groups: open-loop control, which relies on physically realistic models to represent the object, and closed-loop control, which employs less precise models alongside visual data to compute commands. In this work, we present a novel 3D shape control approach that includes the physically realistic Cosserat model into a closed-loop control framework, using vision feedback to rectify errors in real-time. This approach capitalizes on the advantages of both groups: the realism and precision provided by physics-based models, and the rapid computation, therefore enabling real-time correction of model errors, and robustness to elastic parameter estimation inherent in vision-based approaches. This is achieved by computing a deformation Jacobian derived from both the Cosserat model and visual data. To demonstrate the effectiveness of the method, we conduct a series of shape control experiments where robots are tasked with deforming linear objects towards a desired shape.

cs.RO↗