Trajectory Planning in Joint Space for a Pointing Mechanism Based on a Novel Hybrid Interpolation Algorithm and NSGA-II Algorithm

In order to improve the motion stability of a pointing mechanism, the trajectory planning and trajectory optimization were conducted. To obtain better motion stability, the jerk is required continuous. Therefore, higher order polynomial or B-spline are needed and the calculation amount increases in trajectory planning. A novel hybrid interpolation algorithm "7-order polynomial + improved quartic uniform B-spline curve + 7-order polynomial" was proposed for trajectory planning, which cannot only ensure the trajectory passes through all path points but also ensure the jerk is continuous. From the first path point to the second path point and from the penultimate path point to the last path point, 7-order polynomial is chosen as the interpolation algorithm. The intermediate path points are interpolated by improved quartic uniform B-spline curve which is newly proposed. The improved quartic uniform B-spline curve can pass through all path points and does not require complicated calculation. To carry out the trajectory planning of a X-Y pointing mechanism, the kinematic model was derived at first. Secondly, the hybrid interpolation algorithm was presented. Thirdly, the NSGA-II algorithm was applied to the multi-objective optimization which are time, acceleration and jerk. Finally, the trajectory planning experiment was conducted to prove the validity of the proposed hybrid interpolation algorithm. The experimental results show that the pointing accuracy is improved by using the hybrid interpolation algorithm and the NSGA-II algorithm. This hybrid interpolation algorithm for trajectory planning can be applied to other robots as well.