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In this paper, we focus on the issues pertaining to stiffness-oriented cable tension distributionfor a symmetrical 6-cable-driven spherical joint module (6-CSJM), which can be employed to constructmodular cable-driven manipulators. Due to the redundant actuation of the 6-CSJM, three cables areemployed for position regulation by adjusting the cable lengths, and the remaining three cables areutilized for stiffness regulation by adjusting the cable tensions, i.e., the position and stiffness can beregulated simultaneously. To increase the range of stiffness regulation, a variable stiffness device(VSD) is designed, which is serially connected to the driving cable. Since the stiffness model of the6-CSJM with VSDs is very complicated, it is difficult to directly solve the cable tensions from thedesired stiffness. The stiffness-oriented cable tension distribution issue is formulated as a nonlinearconstrained optimization problem, and the Complex method is employed to obtain optimal tensiondistributions. Furthermore, to significantly improve the computation efficiency, a decision variableelimination technique is proposed to deal with the equality constraints, which reduces decision variablesfrom 6 to 3. A comprehensive simulation study is conducted to verify the effectiveness of the proposedmethod, showing that the 6-CSJM can accurately achieve the desired stiffness through cable tensionoptimization.

In this paper, an integrated accuracy enhancement method based on both the kinematic model and the data-driven Gaussian Process Regression (GPR) technique is proposed for a Cable-Driven Continuum Robot (CDCR) with a flexible backbone. Different from the conventional continuum robots driven by pneumatic actuators, a segmented CDCR is developed in this work, which is a modular manipulator composed by a number of consecutive Cable-Driven Segments (CDSs). Based on the unique design of the backbone structure which merely allows 2-DOF bending motions, a two-variable Product-of-Exponential (POE) formula is employed to formulate the kinematic model of the CDCR. However, such an analytic kinematic model is unable to accurately describe the actual deflections of the backbone structure. Therefore, GPR is proposed to compensate the tip error of a CDCR. Compared with other machine learning methods, GPR requires less learning parameters and training data, which makes the learning process computationally efficient. To validate the effectiveness of the proposed integrated accuracy enhancement method, experiments on the actual testbed are conducted. Experimental results show that the CDCR's position and orientation errors are reduced by 68.72% and 51.74%, respectively. INDEX TERMS Cable-driven continuum robot, kinematic modeling, tip error compensation, Gaussian process regression.