绳系卫星轨道转移的最优控制

Optimal Control of Orbit Transfer for a Tethered Subsatellite System

考虑系绳的弹性以及复杂状态和控制约束的作用,研究了绳系卫星面内轨道转移的最优控制问题。借助Gauss伪谱算法,将绳系卫星轨道转移的连续时间最优控制问题离散为大规模动态规划问题,进而利用非线性规划方法进行求解。通过数值模拟计算了子星最优转移轨道及最优控制力。结果表明:在满足相关约束的条件下,通过调节系绳张力可将子星从主星下方转移到上方的平衡位置,精确地实现子星轨道转移,并使得轨道转移过程呈现出良好的光滑性和对称性。最后基于协态映射定理对解的最优性进行了验证。

This article presents a nonlinear optimal control scheme for the orbit transfer problem of a tethered subsatellite model in the orbit plane. The scheme takes into consideration the complex state control constraints and elasticity of tether. A combination of the Gauss pseudospectral method and costate mapping theorem is exploited in this work to find an optimal trajectory that guides the subsatellite from one nominal equilibrium position to another by changing the tensional force of the tether. The nonlinear optimal control problem is solved by first discretizing it and then solving the resulting large-scale optimization problem via nonlinear pro gramming. The optimal control force and transfer trajectory are solved through a case study. Interestingly, the controlled trajectory of the transfer process is geometrically symmetric about the midpoint of the time interval. Finally, the optimality of the solutions is also validated through a brief analysis of costatc information.