In this paper, we treat the point-to-point (PTP) motion of a rotary crane system, whose load attached to a boom moves in the two-dimensional plane, and then propose a feedforward control technique for suppressing the residual sway motion after positioning. In particular, we attempt to add robustness to parameter variations on the proposed feedforward control technique. In the proposed control technique, the trajectory for the PTP motion is expressed by the combination of cycloidal and trigonometric functions. The profile of the generated trajectory depends on the coefficients of the trigonometric function. Thus, we tune the coefficients by a particle swarm optimization algorithm so as to minimize the residual sway motion, in which the objective function for the tuning is defined to consider the robustness to parameter variations. By driving the boom of the rotary crane along the obtained optimal trajectory, the antisway motion can be realized even if the parameter of the system varies, i.e., the proposed method can establish a robust feedforward control. Results obtained from simulations and experiments demonstrate the effectiveness and feasibility of the proposed vibration control technique.