Title: Numerical integration-like algorithm for time-optimal trajectory optimisation of multi-axis motion system based on iterative learning

Authors: Tie Zhang; Cailei Liao; Yanbiao Zou; Zhongqiang Kang; Caicheng Wu

Addresses: School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, China ' School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, China ' School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, China ' School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, China ' School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, China

Abstract: In order to realise the high-velocity and high-precision motion of the multi-axis motion system, a numerical integration-like time-optimal trajectory optimisation algorithm combined with iterative learning is proposed. Based on the established dynamic model of the multi-axis motion system, the mathematical model with time optimisation as the objective function is derived under kinematics and dynamics constraints. The planned trajectory is discretised and the uniform acceleration equation (SUVAT) between any two adjacent discrete points is assumed so that pseudo-velocity planning of the phase plane is carried out by SUVAT equation instead of numerical integration method, after which the optimal solution satisfying the constraints can be obtained. In order to improve the dynamic model and reduce the errors between the calculated and the actual measured torques, a PD-type iterative learning method with forgetting factor is used to continuously update the dynamic model.

Keywords: high-velocity; high-precision; multi-axis motion system; time-optimal control; dynamic model; phase plane; numerical integration; iterative learning; forgetting factor.

DOI: 10.1504/IJAAC.2023.127280

International Journal of Automation and Control, 2023 Vol.17 No.1, pp.91 - 115

Received: 28 Mar 2021
Accepted: 11 Sep 2021
Published online: 30 Nov 2022 *