Data-Driven Stiffness Modeling and Design Optimization of Flexible Backbones for Modular Cable-Driven Continuum Robots

Most bioinspired cable-driven continuum robots (CDCRs) usually employ a flexible backbone to realize the continuous deflection. For the CDCR to merely produce bending motions, its flexible backbone has to be designed with low bending stiffness but high tensile and torsion stiffness. In this article, a pattern-based design approach is employed for the flexible backbone, which adopts rectangle-shaped patterns inspired by elastic couplings. As it is rather difficult to derive accurate analytical stiffness models for such a pattern-based backbone structure with large nonlinear deflections, a novel data-driven stiffness modeling approach is proposed. The Gaussian process regression method is employed to train the stiffness model with respect to structure parameters of the backbone, while the dataset is generated through a commercial finite element analysis software package. To narrow the distribution of the training data and make the predicated stiffness values always positive, the natural logarithm transformation is utilized for data preprocessing, which significantly increases the accuracy of prediction results. The average errors of the bending, tensile, and torsion stiffness between simulation results and predicted results converge to 1.88%, 2.33%, and 2.11%, respectively. The particle swarm optimization algorithm is employed for the structure parameter optimization based on the data-driven stiffness model. The stiffness errors of the optimized flexible backbone between simulation results and experimental results are 5.19%, 19.09%, and 5.38%, respectively. Experimental results show that the average position repeatability and orientation repeatability of a CDCR are 0.8822 mm and 0.0046 rad and the CDCR can carry the 500 g payload.