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.

The newly developed 4PPa-2PaR parallel mechanism has subchains on its limbs, and the imperfect assembly process causes the kinematic error. The conventional matrix-based method is difficult to set up its kinematic error model, as the kinematic constraints cannot be represented by the homogenous transformation matrix intuitively. In this work, the actual kinematic model is established using a vector-based method, considering the nonideal lengths of links and misalignment of active joints’ home sensors. Thereby, the kinematic constraints of the mechanism are intuitively incorporated into the model, and the deviations of kinematic parameters are identified by the Levenberg–Marquardt algorithm. To achieve error compensation using the inverse of the actual kinematic model, a flange with three collinear reflector holders is designed and mounted on the moving platform, and a three-point measurement method is utilized to capture its pose without using a tracker-machine control sensor (T-MAC). Another flange for reflector holders is designed and mounted on the active joint for setting up the base frame so that all measurement data are transformed from the laser tracker’s frame to the base frame to complete the calibration process. Experiments are conducted on the testbed to validate the effectiveness of the proposed calibration method.

Highly flexible continuum arms have been investigated thoroughly. Materials and actuators employed include cables, pneumatic muscles, and also shape memory alloys (SMAs). SMA is a smart material that can be applied to continuum robot due to their intrinsic compliance. It can elongate or contract by applying external forces and return to its original shape when given appropriate current. However, control of the SMA actuated robot is still a challenge. This paper takes inspiration from octopus neurophysiology and designs a hierarchical controller for the SMA based continuum robotic arm.

In this paper, we focus on the issues pertaining to stiffness-oriented cable tension distribution for a symmetrical 6-cable-driven spherical joint module (6-CSJM), which can be employed to construct modular cable-driven manipulators. Due to the redundant actuation of the 6-CSJM, three cables are employed for position regulation by adjusting the cable lengths, and the remaining three cables are utilized for stiffness regulation by adjusting the cable tensions, i.e., the position and stiffness can be regulated 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 the 6-CSJM with VSDs is very complicated, it is difficult to directly solve the cable tensions from the desired stiffness. The stiffness-oriented cable tension distribution issue is formulated as a nonlinear constrained optimization problem, and the Complex method is employed to obtain optimal tension distributions. Furthermore, to significantly improve the computation efficiency, a decision variable elimination technique is proposed to deal with the equality constraints, which reduces decision variables from 6 to 3. A comprehensive simulation study is conducted to verify the effectiveness of the proposed method, showing that the 6-CSJM can accurately achieve the desired stiffness through cable tension optimization.

The unit dual quaternion (UDQ)-based product-of-exponential (POE) formula has achieved efficient kinematic calibration for serial manipulators. However, due to the presence of unknown passive joint displacements, it is difficult to directly establish explicit forward kinematic models for parallel manipulators (PMs). This forms a barrier to subsequent error modeling and compensation. This work establishes a novel UDQ-based forward kinematic model for a PM by utilizing constraints on the identical pose of the moving platform across all its chains. Furthermore, the adjoint transformation of UDQ's twist is derived for PM's error modeling. Notably, an index matrix is introduced to achieve a unified representation of active or passive joint displacement. Thereby, this UDQ-based kinematic error modeling method is applicable to general PMs. In addition, an error compensation method is proposed for a PM using the UDQ-based local POE formula, which incorporates the developed forward kinematic model to adjust active joint displacements. The proposed method offers significant runtime savings compared to the traditional homogeneous-transformation-matrix-based POE formula due to the compact data structure and reduced arithmetic operations.

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.