The use of higher-degree polynomials for trajectory planning with jerk, acceleration and velocity constraints

Abstract

The paper presents a smooth trajectory planning method using higher-degree polynomials. Polynomial functions of acceleration were determined and accurate dependencies were derived for the calculation of polynomial coefficients and motion time in the case of velocity, acceleration and jerk constraints. The paper also presents a way of trajectory planning when a few constraints occur at the same time. To assess the efficiency of the proposed approach, a simulation study has been carried out using MATLAB. The courses of kinematic quantities are presented in the diagrams and compared. The proposed method ensures the continuity of displacement, velocity, acceleration and jerk and can be applied for trajectory planning of various mechanical systems (manipulators, mobile robots, CNC machines, autonomous vehicles).