CAD based trajectory optimization of PTP motions using chebyshev polynomials

Abstract

Trajectory optimization of position-controlled servo systems driving repetitive tasks is very appealing in research as it allows for more performant and efficient machines without any additional investment in hardware. In particular, monoactuator systems with position-dependent system properties have received much attention in the literature as they represent a large part of mechatronic systems and can easily be modeled with existing CAD packages. Although techniques for optimization of the position profile are well documented, most literature is based on the heuristic and iterative optimization of polynomial and piecewise position curves. This results in locally optimal solutions and long calculation times. In this context, the purpose of the present paper is twofold. On the one hand, this paper outlines the theoretical framework for a fast trajectory optimization approach of single degree of freedom (1-DOF) systems with Chebyshev polynomials. On the other hand, a comparison of these solutions with results obtained using stateof-the-art techniques is provided. To do so, system property data is extracted with CAD motion simulations and converted into closed mathematical descriptions using polynomial interpolation. By combining these polynomial system models with a reconditioning and scaling of the trajectory definition, a novel problem formulation is obtained, which allows for fast gradientbased optimization techniques while limiting the risk of getting stuck in a local optimum. In this study, it was found that although substantial savings are achieved with state-of-the-art optimization methods, our proposed method with Chebyshev polynomials results in an extra saving potential of up to 6.7%. The findings also reveal a significant reduction in computational complexity. The latter not only supports the applicability of the proposed technique but also has implications for new system designs where real-time trajectory optimization is of interest.