Kinematically smoothing trajectories by NURBS reparameterization – an innovative approach

Abstract

This paper presents an innovative curve reparameterization method for kinematically smoothing trajectories based on jerk minimization. In this research, not only the trajectory is expressed in terms of a parametric NURBS curve, but also the curve parameter is related to the execution time by means of a NURBS reparameterization function. Meanwhile, an analytical sensitivity analysis is developed to minimize the jerk magnitude of the trajectory in a gradient-based optimization. The advantage of the proposed methodology is that the geometric shape of the trajectory’s path remains unchanged while the jerk is smoothed. Hence, the trajectory will be tracked by the optimized values of velocity, acceleration, and jerk. It would be helpful when the trajectory’s path cannot be changed because of the geometrical limitations or obstacle avoidance scheme. The applicability of the presented approach is also illustrated by some case studies.