Strain-based Cosserat Rod Model for Suspended Cable-Driven Parallel Robots in Construction 3D Printing

Suspended Cable-Driven Parallel Robots (SCDPRs) are gaining prominence as scalable, cost-effective solutions for large-scale robotic 3D printing in construction and manufacturing. However, their performance is hindered by challenges such as cable deformation including sagging and vibration, dynamic variation of cable lengths for actuation, and the complexity of modeling rigid–flexible hybrid systems, all of which lead to significant printhead positioning inaccuracies that degrade print precision. To address these challenges, this work presents a geometric, strain-based Cosserat-rod dynamic model to capture the complex interactions within the hybrid soft-rigid multi-body system. The model incorporates time-varying boundaries of the flexible (soft) links to account for the cable actuation. To improve positioning accuracy, an inverse kinetostatic formulation is employed to compute optimized cable lengths that minimize the end-effector tip error. The proposed approach is evaluated through three representative SCDPR configurations: first, a system benchmarked against a state-of-the-art method to assess modeling accuracy; second, a small-scale experimental prototype demonstrating circular trajectory tracking; and third, a large-scale simulated setup illustrating the feasibility of generating geometrically complex structures in a construction-scale scenario. The results confirm the ability of the proposed model to achieve high tracking accuracy, system stability, and control fidelity. Moreover, the computational efficiency and modularity of the formulation establish it as a promising foundation for future real-time control implementations in additive manufacturing and construction automation.