In this paper we extend the previously introduced notion of closed-loop state sensitivity by introducing the concept of input sensitivity and by showing how to exploit it in a trajectory optimization framework. This allows to generate an optimal reference trajectory for a robot that minimizes the state and input sensitivities against uncertainties in the model parameters, thus producing inherently robust motion plans. We parametrize the reference trajectories with Béziers curves and discuss how to consider linear and nonlinear constraints in the optimization process (e.g., input saturations). The whole machinery is validated via an extensive statistical campaign that clearly shows the interest of the proposed methodology.