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High precision control in PTP trajectory planning for nonlinear systems using on high‐degree polynomial and cuckoo search
Author(s) -
Wu Huifeng,
Sun Danfeng
Publication year - 2018
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2464
Subject(s) - cuckoo search , trajectory , polynomial , control theory (sociology) , nonlinear system , trajectory optimization , degree (music) , kinematics , mathematics , mathematical optimization , computer science , degree of a polynomial , optimal control , control (management) , artificial intelligence , particle swarm optimization , mathematical analysis , physics , classical mechanics , quantum mechanics , astronomy , acoustics
Summary In this paper, in order to fulfill requirements for high precision control, high‐degree polynomial and cuckoo search algorithms are used in point‐to‐point (PTP) trajectory planning for nonlinear systems. The high‐degree polynomial describes the PTP trajectory and the cuckoo search is applied to obtain the coefficients of the high‐degree polynomial with constraints. This method is verified in the hydraulic toggle mechanism. Hamilton's principle and a Lagrange multiplier help establish the dynamic and kinematic equations in the hydraulic toggle mechanism. Position accuracy and the convergence effect of different degrees of polynomials are then compared through experiment. Specifically, this paper discusses the error of the 8‐degree polynomial trajectory between the optimization and practical values and the repeated accuracy of the optimization trajectory, which verify the method's high precision control in regard to the PTP trajectory planning for nonlinear system proposed in this paper. This method could be used in any type of PTP trajectory planning for nonlinear system.