Closed-Form Solution for Time Optimisation of Single-Axis Multi-Point Motion

This paper presents an in-depth study of the S-curve model. Under the constraints of system bandwidth, an efficient and accurate closed-form solution is proposed for the time-optimisation problem of a single actuator passing through multiple position points. In this method, the multi-point motion problem is transformed into a monotonic interval motion problem, and different motion equations are derived according to different motion conditions. Finally, the splicing and matching of acceleration between different intervals are completed through a backtracking mechanism. Since a closed-form solution formula is provided, the entire process of this method is efficient and accurate. This study not only provides a new idea and feasible solution for single-axis multi-point motion, but also contributes an important theoretical derivation to the body of research based on the S-curve model.