Optimal placement of inherent zeros in polynomial-based motion profiles for minimizing residual vibration and travel time under system uncertainties

Various industrial processes require motion profiles that determine machine movement over time for workpiece transfer, with the goal of minimizing transfer time to enhance productivity. However, pursuing the maximum speed can trigger excessive motion-induced vibration, which can reduce the manufacturing efficiency, accuracy and operational lifespan of the system. This study proposes a generalized motion profile optimization method that considers the strategic placement of inherent zeros within the motion profile: each inherent zero contributes to the reduction of residual vibration or optimization of arrival time. By offering freedom to the placement of zeros, four optimization options for polynomial-based motion profiles of each order are proposed, expanding on existing work that offered a single option. All proposed optimization options have closed-form solutions, making them easily applicable to industrial applications. The practical applicability of the suggested methodology is demonstrated through case studies and experiments.