A Predictor-Corrector Algorithm for the Fast Determination of the Wrench-Feasible Workspace of Cable-Driven Parallel Robots

Abstract

In this letter, we present a method of determining the Constant-Orientation Wrench-Feasible Workspace (COWFW) of Cable-Driven Parallel Robots (CDPRs). This workspace is a critical property of CDPRs, as their reach is often limited by their ability to sustain required forces and moments while keeping their cable tensions within acceptable limits. Several manners of determining the COWFW are reported in the literature, among which the brute force method is probably the most popular, the easiest to implement and the slowest, as it consists in determining wrench-feasibility at a grid of points covering the workspace. On the other hand, the ray-tracing method implemented in WireX software is probably the fastest method available; It consists in sampling the COWFW boundary by performing line-searches from a common starting point along predetermined, evenly-spaced directions. The method proposed in this letter is the application to CDPRs of a predictor-corrector algorithm used in computer graphics to quickly sample implicit surfaces In this work, the implicit surface is defined by equating to zero the “capacity margin” an index developed by one of the authors. The predictor-corrector algorithm then “marches” over the implicit surface, triangulating it as it advances. Simulation results show that the determination of the COWFW surface by this technique can be faster than the ray-tracing method in at least some examples, and often yields a triangulation that is more regular. We should note, however, that the implementation of this method is more demanding, it requiring more lines of code than the ray-tracing method.