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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.

A cable-driven manipulator (CDM) has low stiffness and its stiffness identification is a critical issue. This paper focuses on stiffness modeling and identification for a cable-driven spherical joint module (CSJM), whose trajectory is a curve on SO(3). In order to obtain the stiffness of the CSJM, it requires to evaluate the variation of the load against the displacement. However, since the vectors of displacement and load at different poses of the CSJM belong to different vector spaces of SO(3), the algebraic operations between them can not be performed directly. Hence, a Riemannian metric and the Levi-Civita connection are defined on SO(3), so that vectors can be parallel transported from one vector space to another along the trajectory curve. Consequently, the covariant derivative of the load with respect to the displacement is defined on SO(3) to establish the stiffness model. The resultant stiffness matrix is proved to be symmetric for a conservative system. In this way, the stiffness model with the system parameters of the CSJM is derived based on the kinetostatic analysis. Due to a part of the system parameters can not be accurately known, a feasible stiffness identification method is proposed based on the approximation of the covariant derivative, which merely require to measure the poses and loads of the CSJM. The experiment on the actual testbed validates the practical appeals of the proposed stiffness model and associate identification method. INDEX TERMS Cable-driven spherical joint module, stiffness modeling, stiffness identification, force/torque sensor, Riemannian manifold.

Inspired by the structure of human arms, a modular cable-driven human-like robotic arm (CHRA) is developed for safe human–robot interaction. Due to the unilateral driving properties of the cables, the CHRA is redundantly actuated and its stiffness can be adjusted by regulating the cable tensions. Since the trajectory of the 3-DOF joint module (3DJM) of the CHRA is a curve on Lie group SO(3), an enhanced stiffness model of the 3DJM is established by the covariant derivative of the load to the displacement on SO(3). In this paper, we focus on analyzing the how cable tension distribution problem oriented the enhanced stiffness of the 3DJM of the CHRA for stiffness adjustment. Due to the complexity of the enhanced stiffness model, it is difficult to solve the cable tensions from the desired stiffness analytically. The problem of stiffness-oriented cable tension distribution (SCTD) is formulated as a nonlinear optimization model. The optimization model is simplified using the symmetry of the enhanced stiffness model, the rank of the Jacobian matrix and the equilibrium equation of the 3DJM. Since the objective function is too complicated to compute the gradient, a method based on the genetic algorithm is proposed for solving this optimization problem, which only utilizes the objective function values. A comprehensive simulation is carried out to validate the effectiveness of the proposed method.

A multi-link cable-driven robot (MCDR) usually has a large number of redundant actuating cables due to its modular cable routing scheme. To reduce the number of actuating cables while keeping the advantages of the modular MCDRs, a hybrid modular cable routing method is proposed, in which some actuating cables are co-shared by adjacent cable-driven joints. Consequently, the total number of actuating cables can be reduced to n + 1 for an n-degree-of-freedom (n-DOF) MCDR. Focusing on MCDRs composed of identical 2-DOF cable-driven universal joint modules, the performance of the MCDR with the hybrid modular cable routing scheme is evaluated. It is concluded that: 1) the wrench-closure workspace of an MCDR with the hybrid modular cable routing scheme remains unchanged compared to the conventional modular cable routing scheme; 2) the maximal joint speed is inversely proportional to the total number of joint modules that co-share one actuating cable; and 3) the loading capability of an MCDR is a monotone decreasing function of the number of co-shared actuating cables. To verify the conclusions obtained, computer simulations are conducted on an MCDR with different cable routing schemes. Besides, the hybrid modular cable routing with alternatively co-shared actuating cables is an ideal cable routing scheme as it has the minimum loss of performance on motion speed and loading capability.INDEX TERMS Cable-driven robot, cable routing, workspace analysis, motion speed, loading capability.

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