Navigating the wrench-feasible C-space of cable-driven hexapods

Abstract

Motion paths of cable-driven hexapods must carefully be planned to ensure that the lengths and tensions of all cables remain within acceptable limits, for a given wrench applied to the platform. The cables cannot go slack—to keep the control of the platform—nor excessively tight—to prevent cable breakage—even in the presence of bounded perturbations of the wrench. This paper proposes a path planning method that accommodates such constraints simultaneously. Given two configurations of the platform, the method attempts to connect them through a path that, at any point, allows the cables to counteract any wrench lying inside a predefined uncertainty region. The resulting C-space is placed in correspondence with a smooth manifold, which allows defining a continuation strategy to search this space systematically from one configuration, until the second configuration is found, or path non-existence is proved by exhaustion of the search. The approach is illustrated on the NIST Robocrane hexapod, but it remains applicable to general cable-driven hexapods, either to navigate their full six-dimensional C-space, or any of its slices.