An Atlas-Based Approach to Planar Variable-Structure Cable-Driven Parallel Robot Configuration-Space Representation

Variable-structure cable-driven parallel robots (VSCR) are a new class of cable robots that are able to cover nonconvex installation spaces by permitting collisions between cables and fixed objects in the environment. In this article, we show how the configuration space of a general planar VSCR can be represented as an organized set of partially overlapping regions of constant structure. The benefit of this representation, which we refer to as the "structure atlas, " is that it allows any techniques from the established cable-driven parallel robot literature to be applied locally, greatly simplifying the modeling complexity associated with VSCRs. A complete method for how such a representation can be constructed is provided, which includes identifying the set of reachable kinematic structures for a given VSCR and the area where each structure is active. We then give specific examples of how this new representation can be used for performing VSCR workspace analysis and directly solving the VSCR inverse kinematics problem. Our results are demonstrated with the aid of simulated and experimental results.