Trajectory Tracking for Cable-driven Underactuated Manipulator Based on Udwadia-Kalaba Theory

The explicit dynamic model of the cable-driven underactuated manipulator is established to calculate the constraint force by second-order constraints using the Udwadia-Kalaba theory and taking into account the trajectory tracking requirements of the cable-driven underactuated manipulator as the external constraints. Following the decomposition of the constraint force, the analytical expression for the cable tension is obtained. Furthermore, the numerical simulation in MATLAB shows that, when affected by the previously calculated cable tension, the manipulator's tracking trajectory may precisely match the requirements. This approach lessens modeling complexity without the Lagrangian multiplier compared to conventional Lagrangian modeling techniques.