# SMOOTH AND TIME OPTIMIZATION TRAJECTORY PLANNING FOR ROBOTS USING POLYNOMIAL INTERPOLATION

### Abstract

In this study, the trajectory planning for robots using polynomials is investigated. The polynomials used to plan the robot’s trajectory include multiple cubic polynomials, multiple quintic polynomials, and one higher-order polynomial for the entire trajectory segment with the requirement of smooth motion, i.e., maintaining continuity of velocity, acceleration, and jerk within allowable limits. The traveling time was also an optimized factor. The application results for a parallel robot show that the trajectory using multiple cubic polynomials has the shortest traveling time. However, using multiple cubic polynomials has the disadvantage of a discontinuous jerk. Using a single higher-order polynomial for the entire trajectory takes about 12 % more time than multiple cubic polynomials but has the advantage of a continuous jerk.

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