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Numerous types of input shapers have been developed to reduce motion-induced vibration. Many of the shapers are designed using non-linear optimisation methods that can be challenging to implement and do not guarantee a global minimum solution. This paper unifies the solution of different types of input shapers into a single computational framework based on linear optimisation techniques. Two methods for computing a variety of digital input shapers are presented. The first method is a multi-level optimisation that enables both primary and secondary performance measures to be simultaneously optimised. The second method is a computationally efficient technique for computing very robust shapers.