Costate Estimation With Bezier-Curve-Based Shaping Approach for Fuel-Optimal Multisatellite Formation Reconfiguration

A fast costate estimation technique with shaping-based method is applied to the indirect optimization of fuel-optimal multisatellite formation reconfiguration. The Bezier-curve-based shaping approach is able to solve the approximate optimal trajectory rapidly, which is to estimate the costate by being discretized at Gauss points and substituted into the discrete first-order optimality condition. The performance of costate estimation is verified in three-satellite formation reconfiguration and six-satellite formation configuration initialization. Compared with the direct method's results, the costate estimation can lead to optimal solutions of indirect optimization and only spend 5.8% and 5.9% calculation time of direct method.