A novel methodology for saturation setting in parabolic ramp profiles for trajectory planning

Abstract This paper presents a novel methodology for optimizing various kinematic (velocity, acceleration, and jerk) and kinetic (required force, mechanical power, and energy consumption) variables without the need to preselect and configure the drive system elements. The approach is based on the saturation adjustment of parabolic ramp velocity profiles in trajectory planning tasks. To develop this methodology, a mathematical model of the variables to be optimized was formulated, accounting for the potential presence of non-inertial constant loads that the drive system must overcome. The variation of these variables over the cycle time was analyzed, as well as the influence of the selected profile saturation value on their behavior. The methodology was then applied in a case study. The findings indicate that the absence of the proposed methodology resulted in kinematic variable increases ranging from 50 to 350% relative to their optimal values. Likewise, kinetic variables increased by up to 366% compared to their optimal values when the methodology was not implemented. The proposed methodology is applicable to transport systems, Cartesian manipulators, motion control of mobile robots, and mechatronic systems in which the primary non-inertial forces are constant.