Time-jerk optimal deployment trajectory planning of deployable parabolic cylindrical antenna

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.