A real-time capable force calculation algorithm for redundant tendon-based parallel manipulators

Tendon-based parallel manipulators with n d.o.f. use at least m = n + 1 tendons to guide the end effector along a given trajectory. Since tendons can only transmit limited and tractive forces, it is essential to apply a valid tendon force distribution. Due to safety and precision requirements, a combined position and force control is needed where the force calculation delivers the desired tendon force distributions. The high dynamic potential of the robot demands for realtime capable algorithms. To avoid steps in the motor torques the calculated tension force distributions also have to be continuous along the trajectory. In this paper, a new algorithm for tendon force distribution calculations capable for usage on a realtime system is proposed and its continuity is proven.