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This work considers the design of point-to-point input trajectories that result in minimal residual vibration of flexible motion systems. The design is based on a recently developed optimization framework for polynomial spline design. This framework is based on linear programming and automatically selects the optimal number and location of the spline knots, while also allowing the designer to consider input constraints and robustness against parametric uncertainty and unmodeled dynamics. Simulation and experimental results are presented for a two-degree-of-freedom (2-DOF) test setup and compared to two literature benchmark methods.