A dimension-reduction-based real-time tension distribution algorithm for a reconfigurable nine-cable-driven parallel robot

In cable-driven parallel robots, increasing the number of cables can enlarge the workspace but also increases actuation redundancy, making online tension distribution more difficult. This paper proposes a dimension-reduction-based real-time tension distribution algorithm for a reconfigurable nine-cable-driven parallel robot (9-CDPR) with a 6-DOF end-effector. The robot combines a conventional 8-CDPR with a movable ninth-cable exit point, allowing the ninth cable to remain approximately vertical and bear the main gravitational load. Compared with a fixed-exit-point 9-CDPR, the reconfigurable design increases the estimated wrench-feasible workspace volume by 55.76% under identical tension limits. For the three-redundant 9-CDPR, the original three-dimensional tension feasible region is reduced to two two-dimensional sectional TFRs, and the final tension solution is obtained by convex averaging. Simulations show that the proposed method produces continuous tension solutions consistent with the full-TFR centroid method, while reducing the average computation time to 0.44 ms. Compared with a recent three-redundant TDA [1], the average computation time and FLOPs are reduced by 74.2% and 76.5%, respectively. Prototype experiments confirm 1 ms real-time implementation. These results indicate that the proposed method provides a practical solution for real-time tension distribution of reconfigurable 9-CDPRs with three degrees of actuation redundancy.