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This paper introduces the X-ACTA algorithm, an extended version of the Analytic Center method, designed to determine cable tensions for Cable-Driven Parallel Robots (CDPRs) operating beyond their Wrench-Feasible Workspace (WFW). The method maintains continuous and differentiable tension profiles while ensuring fast convergence to a unique solution, significantly reducing wrench errors compared to existing slack-based approaches. Numerical experiments validate its superiority in smoothness and performance, highlighting its potential for enhancing CDPR capabilities in demanding scenarios.
Achieving smooth and differentiable cable tension profiles outside the WFW could revolutionize the operational limits of Cable-Driven Parallel Robots.
Steering Cable-Driven Parallel Robots (CDPRs) beyond their Wrench-Feasible Workspace (WFW) augments their capabilities in challenging scenarios such as during aggressive maneuvers or following a cable failure. In this context, although the determination of cable tensions is a well-studied topic, only a few approaches address these scenarios. Therefore, this paper introduces an extended version of the Analytic Center method as a criterion for selecting cable tensions outside the WFW while maintaining differentiability and including non-linear constraints. Notably, the proposed method maintains continuous and differentiable tension profiles, ensures fast real-time convergence to a unique solution, and, in contrast to other slack-based formulations, relegates wrench errors to a negligible area of the WFW. Its superiority in terms of smoothness and wrench error is confirmed via Pareto dominance with respect to the leading state-of-the-art method. Lastly, the effectiveness of the method is demonstrated through numerical experiments.
