Optimization of Time-Open Constrained Lambert Rendezvous Using Interval Analysis

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Optimization of Time-Open Constrained Lambert Rendezvous Using Interval Analysis

Chen, Tong / van Kampen, E. / Yu, H. / Chu, Q. P.

By defining a parking time and a transfer time, a time-open constrained Lambert rendezvous problem is proposed in this paper. The purpose of optimization is to minimize the velocity increment for the orbital rendezvous. The interval branch and bound optimization algorithm is introduced for solving a rendezvous optimization problem with strong nonlinearity and nonconvexity. A numerical example is undertaken to validate the interval optimization algorithm. The results indicate that although the global optimal solution for the time-open constrained Lambert rendezvous problem can’t be found by using only the interval algorithm in the restricted hardware environment because of the inevitable influence of interval dependency and the complex calculation for the cost function, the interval algorithm can narrow the search space and split the feasible space into many small subspaces. Combining the gradient-based optimization method, an improved interval algorithm is used to find the minimal velocity increment for orbital rendezvous, which is better than the optimal solution using the genetic algorithm.