Cable-driven parallel robots (CDPRs) are under-actuated if they use a number of cables smaller than the degrees of freedom (DoF) of the end-effector (EE). For these robots, the constraint deficiency on the EE may lead to undesirable EE oscillations along the path that it is supposed to track. This paper proposes a trajectory-planning method for underactuated CDPRs which is robust against dynamic-model uncertainties or parameter variation, aiming at minimizing EE oscillations along a prescribed path. Oscillation reduction and robust-ness are achieved by means of Zero-Vibration Multi-Mode Input Shaping and Dynamic Scaling of a reference trajectory. Simulation results show the effectiveness of the method on a 3-cable 6-DoF robot.