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考虑系绳质量、系统质心变化及状态、控制约束,基于Lagrange方程给出了圆轨道条件下空间绳系网捕系统三维动力学模型。推导得到了零相对速度条件下的安全捕获末端条件,研究了面内安全捕获策略下的非线性能量最优控制问题。为保证方法的适用性,基于Legendre伪谱法将连续时间最优控制问题离散为标准的非线性动态规划问题。最后在考虑捕获控制前初始面外角偏差分别为5°和15°的情况下,通过数值仿真验证了该方法的有效性。
Considering the quality of tether, the change of state of mass center, the state and the control constraints, a three-dimensional dynamic model of the space networked trawling system under circular orbit was given based on Lagrange equation. The end-of-flight conditions of zero-relative velocity are deduced, and the optimal control of nonlinear energy under the in-plane safety strategy is studied. To ensure the applicability of the method, the continuous time optimal control problem is discretized as a standard nonlinear dynamic programming problem based on Legendre pseudospectral method. Finally, the numerical results show that the proposed method is validated when the initial angular errors are 5 ° and 15 °, respectively.