A Spatial Biarc Method for Inverse Kinematics and Configuration Planning of Concentric Cable-Driven Manipulators

Superior dexterity and extreme flexibility are typical advantages for concentric cable-driven manipulators working in confined spaces. However, its inverse kinematics and configuration planning are very complicated. In this article, we propose a spatial biarc method for the above problem. The distinguishing feature of this method is that input parameters are two positions and two direction vectors in three-dimensional (3-D) space, and the output is a reasonable spatial biarc for controlling a concentric cable-driven manipulator in 3-D space. This method has the following three advantages. First, the positions and direction vectors of the base and inner distal tip are considered simultaneously. In addition, the length and ratio of the overlapped section and separated section can be adjusted by changing the length of the direction vectors. Furthermore, by judging the angular value of the direction vectors, one can predetermine whether the spatial configuration of the entire arm is C- or S-shaped. The proposed method realizes the parameterization of a concentric cable-driven manipulator, which makes it convenient to intuitively control the manipulator to achieve interference-free motion trajectory planning in confined spaces. Finally, trajectory tracking inspections are simulated and experimentally executed. It can be seen from results that the proposed spatial biarc method can provide reasonable solutions for concentric cable-driven manipulators. The method is especially favorable in terms of 3-D-pose-determination problem and trajectory-planning problem. It can also be applied to other manipulators with similar configurations. Without loss of generality, when the given points and direction vectors are coplanar, the proposed spatial biarc method can be transformed to a planar biarc method.