Optimal Control Approach to Lambert’s Problem and Gibbs’ Method

This paper presents the optimal control approach to solve both Lambert’s problem and Gibbs’ method, which are commonly used for preliminary orbit determination. Lambert’s problem is reinterpreted with Hamilton’s principle and is converted to an optimal control problem. Various extended Lambert’s problems are formulated by modifying the weighting and constraint settings within the optimal control framework. Furthermore, Gibbs’ method is also converted to an extended Lambert’s problem with two position vectors and one orbit energy with the help of the proposed orbital energy computation algorithm. The proposed extended Lambert’s problem and Gibbs’ method are numerically solved with the Lobatto pseudospectral method, and their accuracies are verified by numerical simulations.