Abstract
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.
Highlights
Cable-driven manipulators (CDMs) are a special class of mechanisms in which cables are employed as the driving elements
We focus on the issue of stiffness-oriented cable tension distribution for a symmetrical
Denote Kdes = {kdes(ij) } ∈ R3×3 (i, j = 1, 2, 3) as the desired stiffness matrix of the 6-cable-driven spherical joint module (6-cable-driven spherical joint module (CSJM)) at a given pose Rdes, and Kact = {kact(ij) } ∈ R3×3 (i, j = 1, 2, 3) as the actual stiffness matrix, a desired stiffness matrix is computed with the given cable tensions according to the stiffness model (21) and an actual stiffness matrix is computed with the actual cable tensions or measured by the equipments
Summary
Cable-driven manipulators (CDMs) are a special class of mechanisms in which cables are employed as the driving elements. In [36], the issue of stiffness-oriented cable tension distribution is studied and a gradient projection based method is developed to regulate the stiffness of a CDM by adjusting cable tensions. This method employs the determinant of the stiffness matrix as the cost function, rather than all entries of the stiffness matrix. The major merit of the proposed stiffness-oriented cable tension distribution method is that it provides an effective way to achieve accurate stiffness regulation and position control simultaneously
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