Rigid robots have found wide-ranging applications in manufacturing automation, owing to their high loading capacity, high speed, and high precision. Nevertheless, these robots typically feature joint-based drive mechanisms, possessing limited degrees of freedom (DOF), bulky structures, and low manipulability in confined spaces. In contrast, continuum robots, drawing inspiration from biological structures, exhibit characteristics such as high compliance, lightweight designs, and high adaptability to various environments. Among them, cable-driven continuum robots (CDCRs) driven by multiple cables offer advantages like higher dynamic response compared to pneumatic systems and increased working space and higher loading capacity compared to shape memory alloy (SMA) drives. However, CDCRs also exhibit some shortcomings, including complex motion, drive redundancy, challenging modeling, and control difficulties. This study presents a comprehensive analysis and summary of CDCR research progress across four key dimensions: configuration design, kinematics and dynamics modeling, motion planning, and motion control. The objective of this study is to identify common challenges, propose solutions, and unlock the full potential of CDCRs for a broader range of applications.

A Cable-Driven Continuum Robot (CDCR) that consists of a set of identical Cable-Driven Continuum Joint Modules (CDCJMs) is proposed in this paper. The CDCJMs merely produce 2-DOF bending motions by controlling driving cable lengths. In each CDCJM, a pattern-based flexible backbone is employed as a passive compliant joint to generate 2-DOF bending deflections, which can be characterized by two joint variables, i.e., the bending direction angle and the bending angle. However, as the bending deflection is determined by not only the lengths of the driving cables but also the gravity and payload, it will be inaccurate to compute the two joint variables with its kinematic model. In this work, two stretchable capacitive sensors are employed to measure the bending shape of the flexible backbone so as to accurately determine the two joint variables. Compared with FBG-based and vision-based shape-sensing methods, the proposed method with stretchable capacitive sensors has the advantages of high sensitivity to the bending deflection of the backbone, ease of implementation, and cost effectiveness. The initial location of a stretchable sensor is generally defined by its two endpoint positions on the surface of the backbone without bending. A generic shape-sensing model, i.e., the relationship between the sensor reading and the two joint variables, is formulated based on the 2-DOF bending deflection of the backbone. To further improve the accuracy of the shape-sensing model, a calibration method is proposed to compensate for the location errors of stretchable sensors. Based on the calibrated shape-sensing model, a sliding-mode-based closed-loop control method is implemented for the CDCR. In order to verify the effectiveness of the proposed closed-loop control method, the trajectory tracking accuracy experiments of the CDCR are conducted based on a circle trajectory, in which the radius of the circle is $55\mathrm{mm}$. The average tracking errors of the CDCR measured by the Qualisys motion capture system under the open-loop and the closed-loop control are 49.23 and $8.40\mathrm{mm}$, respectively, which is reduced by 82.94%.

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.