Efficient Planning and Solving Algorithm of S -Shape Acceleration and Deceleration

Abstract

$\text{S}$ -shape acceleration and deceleration are the most widely used flexible acceleration and deceleration method in the current CNC system, but its velocity solution equation contains irrational terms, which create a more complicated solution process. When analyzing the solution process of the $\text{S}$ -shape acceleration and deceleration directly, using a traditional numerical solution method, the phenomenon of “solving the interval jump” arises, which is the main reason for low efficiency and poor stability of the solution. According to the $\text{S}$ -curve profile and solution, the concept of separating the curve profile recognition from the velocity solution was proposed, and a method of quickly identifying the interval of the solution location was introduced. Through the method mentioned above, the complete acceleration and deceleration curve parameters can be obtained through a one-time plan and a one-time solution, and the solution efficiency and stability are guaranteed; solving the Newton problem depends too much on the initial value of Newton velocity, which not only retains the speed advantage of the Newton method but also uses the downhill factor to ensure its convergence. Through the simulation comparison and analysis, the efficiency, stability, and universality of the method are verified.