In order to realize the flexible capture of noncooperative targets, a variable-stiffness planning method considering both the overall configuration and cable tension for a hyper-redundant manipulator is proposed in this article. First, combining its kinematics and statics, an analytical stiffness model of the hyper-redundant manipulator is developed to evaluate its stiffness. The overall configuration and cable tension of the hyper-redundant manipulator are both identified as main factors that affect the stiffness. Then, a concept of configuration-stiffness mesh and tension-stiffness mesh is proposed to characterize the stiffness trend which can be optimized by active control points. On one hand, the gradient projection method is used to change the overall configuration of the hyper-redundant manipulator to optimize its stiffness. On the other hand, the cascade proportional integral differential control law is used to change the cable tension of the hyper-redundant manipulator to optimize its stiffness. Finally, simulations and experiments are carried out to validate the analytical stiffness model and variable-stiffness planning method considering both the overall configuration and cable tension for hyper-redundant manipulators.

Cable-driven manipulators, characterized by slender arms, dexterous motion, and controllable stiffness, have great prospects for application to capture on-orbit satellites. However, it is difficult to achieve effective motion planning and stiffness control of cable-driven manipulators because of the coupled relationships between cable lengths, joint angles, and reaction forces. Therefore, a convolutional dynamic-jerk-planning algorithm is devised for impedance control of variable-stiffness cable-driven manipulators. First, a variable-stiffness cable-driven manipulator with universal modules and rotary quick-change modules is designed to overcome difficulties related to disassembly, installation, and maintenance. Second, a convolutional dynamic-jerk-planning algorithm is devised to overcome the discontinuity and shock problems of the manipulator’s velocity during intermittent control processes. The algorithm can also make acceleration smooth by setting jerk dynamically, reducing acceleration shock and ensuring the stable movement of the cable-driven manipulator. Third, the stiffness of the cable-driven manipulator is further optimized by compensating for the position and velocity of drive cables by employing position-based impedance control. Finally, the prototype of the variable-stiffness cable-driven manipulator is developed and tested. The convolutional dynamic-jerk-planning algorithm is used to plan the desired velocity curves for velocity control experiments of the cable-driven manipulator. The results verify that the algorithm can improve the acceleration smoothness, thereby making movement smooth and reducing vibrations. Furthermore, stiffness control experiments verify that the cable-driven manipulator has ideal variable stiffness capabilities.

This article presents a segment-progress statics method for configuration prediction or force sensing of concentric cable-driven manipulators. First, the statics model of the whole system was constructed by progressively analyzing from local segments to the whole. This statics modeling method reduces the complexity of the model and considers the most common forces and moments. Second, a solving flow is proposed based on the iteration-correction strategy for configuration prediction or force sensing. This strategy provides a new idea for the analysis of the static friction direction when the statics model is used for quasi-static prediction. Simulations and experiments show that the proposed segment-progress statics method is effective for configuration prediction or force sensing of concentric cable-driven manipulators. Moreover, the effect of the friction gain on the accuracy of statics model is found by analyzing the curvature of the manipulator. The piecewise constant curvature (PCC) assumption is also concluded to be only applicable to small end forces but not to large end forces for concentric cable-driven manipulators.