Two guidance schemes (i) fuel-optimal (ii) energy-optimal to realize soft landing at a desired location on the moon are developed using the optimal control laws. The optimal control laws are obtained by solving a two-point boundary value problem formulated based on Pontryagin’s principle. The guidance laws, adapted from the optimal control laws, are obtained as a function of unknown co-state variables. Differential Transformation (DT) technique is employed to determine the unknown co-states at each time instant of landing trajectory using the information on the current vehicle state, target landing site (loaded on-board apriori) and the time-to-go. The numerical integration of co-state dynamics is avoided due to the DT based approach. The time-to-go, a critical parameter for any guidance scheme, is computed and updated real time using a simple strategy which uses the current and end states. The simple strategy for time-to-go works well even when the shape of the trajectory is nonlinear. Extensive analysis is carried out to evaluate and compare the proposed guidance schemes. Further, the proposed schemes are compared with other popular guidance schemes. The DT based proposed schemes help quantify the landing masses for fuel-optimal and energy-optimal objectives. Other features of the proposed schemes are that they do not assume constant gravity field and independent of reference trajectory.

使用最佳控制定律，开发了两种制导方案（i）燃料最优（ii）能量最优以实现在月球上期望位置的软着陆。通过求解基于庞特里亚金原理的两点边值问题，可以获得最优控制律。从最佳控制定律得到的指导定律是作为未知共态变量的函数而获得的。差分变换（DT）技术用于使用有关当前车辆状态，目标着陆点（车载先验负载）和到达时间的信息来确定着陆轨迹的每个时刻的未知共态。由于基于DT的方法，避免了共态动力学的数值积分。持续时间，是任何指导方案的关键参数，使用一个使用当前和最终状态的简单策略实时计算和更新。即使轨迹的形状是非线性的，简单的走时策略也能很好地发挥作用。进行了广泛的分析，以评估和比较所提出的指导方案。此外，将所提出的方案与其他流行的指导方案进行比较。基于DT的提议方案有助于量化着陆质量，以达到燃料最佳和能量最佳的目标。所提出的方案的其他特征是它们不假定恒定的重力场并且独立于参考轨迹。所提出的方案与其他流行的指导方案进行了比较。基于DT的提议方案有助于量化着陆质量，以达到燃料最佳和能量最佳的目标。所提出的方案的其他特征是它们不假定恒定的重力场并且独立于参考轨迹。所提出的方案与其他流行的指导方案进行了比较。基于DT的提议方案有助于量化着陆质量，以达到燃料最佳和能量最佳的目标。所提出的方案的其他特征是它们不假定恒定的重力场并且独立于参考轨迹。