Initial Value Optimization
Author: Tianjiang Says
Website: https://cislunarspace.cn
Definition
Initial value optimization is the process of finding suitable initial conditions for orbit computation using optimization algorithms. In the context of DRO orbit design, the Differential Evolution (DE) algorithm is used to search for initial values that converge to the desired periodic orbit in the ephemeris model.
Challenge
Computing DRO orbits in the ephemeris model requires good initial guesses because:
- The ephemeris model includes many perturbations (Sun, planets, solar radiation pressure)
- The CR3BP periodic orbit is not exactly periodic in the ephemeris model
- Poor initial guesses lead to divergence of the differential correction process
DE-Based Approach
- Define the search space: initial state variables (position, velocity) and orbital period
- Generate a population of candidate initial values
- Evaluate each candidate by propagating and measuring orbit quality (closure error, stability)
- Evolve the population using DE operators (mutation, crossover, selection)
- Iterate until convergence to high-quality initial values
Advantages
| Advantage | Description |
|---|---|
| Global search | Avoids local optima in the initial value space |
| Robustness | Less sensitive to the choice of initial population |
| Parallelizable | Population evaluation can be parallelized |
| Derivative-free | No need for gradient computation |
Related Concepts
- Differential Evolution
- Differential Correction Method
- Two-Level Differential Correction
- Distant Retrograde Orbit (DRO)
References
- Chen Yuju. DRO Orbit Design and Control Research for Cislunar Space Situation Awareness[D]. 2024.