Non-Iterative Positive Constrained Control of Cable-Driven Parallel Robots

In cable-driven parallel robots (CDPRs), the controller should generate positive output forces, as cables only support tensile forces. In fully-constrained CDPRs, positive tension distribution in cables is guaranteed using optimization-based techniques, which have unpredictable worst-case computation time. Furthermore, the optimization-based methods fail to handle situations where the initial pose of the end-effector is beyond the wrench-feasible workspace (WFW). To address the existing problems, we introduce a new representation of the dynamic model of CDPRs by including cable tension positiveness as an inherent part of the dynamic, using an absolute function. This leads to a non-affine dynamic model, which is then converted to the affine form, for which a robust super-twisting sliding mode controller is designed. The stability of the closed-loop system is guaranteed via the Lyapunov direct method, where H1 asymptotic stability is proved with parameters derived by solving a linear matrix inequality. The superiority of the proposed method is validated in both simulation and experiment. The analytical nature of the method also allows dramatic improvement in the computation time of the control compared to the optimization-based methods in the literature. Additionally, it shows suitable performance at the boundary of the WFW while conventional methods fail to operate.