Direct/Indirect Method

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A hybrid trajectory optimization method combining indirect calculus of variations (costate equations from Pontryagin's minimum principle) with direct transcription, using direct methods to generate initial guesses and indirect methods for refinement.

Application Value

The direct/indirect method leverages the computational efficiency of direct transcription for initial guess generation while using indirect methods based on Pontryagin's minimum principle for high-accuracy refinement. This hybrid approach avoids the sensitivity issues of pure indirect methods (which require good initial guesses for costates) while achieving higher accuracy than pure direct methods. It is widely used in low-thrust cislunar trajectory optimization where accurate convergence to fuel-optimal or time-optimal solutions is critical.

References

  • Yang - 2007 - Earth-moon trajectory optimization using solar electric propulsion
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Contributors: ouyangjiahong, Ou Yang Jiahong