Abstract
A time-jerk optimal deployment trajectory planning method of a large cable-strut deployable parabolic cylindrical antenna is proposed. First, in order to decouple the complex multi-loop mechanisms, the multi-loop basic mechanism of the deployable support structure is split into three single-loop linkages, and the geometric constraint model is established based on the Denavit–Hartenberg method. Then, the kinematic model with jerk characteristics of the basic mechanism is obtained by differentiation. By considering the basic mechanism into a motion element, the kinematic model of the deployable support structure is also established based on matrix coding and motion synthesis theory. Second, by using cubic splines and considering the comprehensive optimal performance of deployment time and system jerk, an antenna deployment trajectory optimization model is established. At last, for obtaining a high precision and stable optimal solution rapidly, the non-dominated sorting genetic algorithm-II is improved by introducing the expected solution preserving strategy. The experimental results show that the proposed approach is able to effectively solve real-parameter multi-objective problems and has better performance on convergence, diversity, and the degree of controlling self-adaptation. The optimal trajectory is efficient and has a smooth kinematic performance.
Highlights
For the convenience of analyzing, the basic mechanisms of the deployable support structure are numbered in a matrix, as shown in
The multi-loop basic mechanism of the deployable support structure is split into three single-loop linkages, and the geometric constraint model is established based on the D–H method
The kinematic model with jerk characteristics of the basic mechanism is obtained by differentiation
Summary
The optimization design of the antenna deployment trajectory needs an accurate kinematic model with jerk characteristics. Liu et al. divided the multi-loop mechanism into several single-loops and obtained the displacement model based on the complex number method. For a parallel mechanism with sub-closed-chains based on the general screw All these studies are for the specific mechanism, and the kinematic modeling method with jerk characteristics of the multi-loop mechanism has still not been presented. In this study, the multi-loop basic mechanism is first split into three single-loop linkages based on the constraint invariant principle and the Denavit–Hartenberg (D–H) method is used to establish the corresponding geometric constraint models. The mechanism gets selflocked in the deployed state, and the mesh reflector that is connected at the point M and point N is in the tension state
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