A Tension Distribution Algorithm for Cable-Driven Parallel Robots Operating Beyond their Wrench-Feasible Workspace

One of the main concerns in the control of over-constrained cable driven parallel mechanisms is the handling of the tension distribution, which is crucial to the proper mechanism behaviour. For example, it dictates the power consumption and stiffness of the mechanism. One problem that remains to be addressed is the handling of cable tensions when the end-effector moves beyond its wrench-feasible workspace, a situation that can arise when the robot is used as a haptic interface. Most existing algorithms are capable of determining whether a specified wrench is unfeasible, but cannot return a suitable second-best tension distribution in such situations. This paper presents an algorithm based on quadratic programming that is capable of handling these situations in real time. The algorithm provides the exact tension distribution for exerting the prescribed wrench when the end-effector is inside the robot workspace. Moreover, when the end-effector is outside of the robot workspace, the algorithm returns a tension distribution that approximately generates the prescribed wrench. The effectiveness of the algorithm is first illustrated using the simulation of a simple cable-driven parallel robot (CDPR). Experimental results are then provided for an eight-cable six-degree-of-freedom CDPR using a real-time implementation.