Efficient Inverse Kinematics and Planning of a Hybrid Active and Passive Cable-Driven Segmented Manipulator

A cable-driven segmented manipulator (CDSM) has superior dexterity for operations in confined space due to its light-slender body and redundant degree of freedoms (DOFs). However, its inverse kinematics resolving and configuration planning are very challenging due to the complex structure and strict constraints. In this article, we propose a two-layer geometric iteration (TLGI) method for inverse kinematics resolving and configuration-constrained Cartesian path planning. The computation efficiency is largely improved and singularities are avoided. First, the end-effector attitude is decomposed into a direction vector and a rotation angle. The former and the end-effector position are combined into state variables of the inner layer, and the latter is treated separately as the state variable of the outer layer. Then, the TLGI method enables to rapidly reach the desired 6-DOF pose by two-layer iterations, i.e., the inner and outer loop iteration. Second, during the inner loop iteration, the CDSM is modeled as an equivalent articulated arm whose end-effector position and direction is the same as that of CDSM, but its links length and joint angles depend on the current configuration of CDSM. Then, the efficient forward and backward reaching inverse kinematics (FABRIKs) method is extended to apply on CDSM so that it can fast reach the inner state variables. During the outer loop iteration, three different rotation cases, i.e., the rotating around the end, root, and both end and root, are designed to switch automatically to reach the outer state variable iteratively. Moreover, by parameterizing geometric constraints of the environment, a TLGI-based configuration-pose simultaneous planning method is also put forward to efficiently achieve additional configuration constraints for operations of CDSM in confined space. Finally, the proposed method is verified by both the simulations and experiments.