Constellation Optimization
Multi-objective evolutionary algorithms for deployer satellite constellation design
Summary
- Multi-objective design of debris remediation constellations.
- Forward-only V3 pipeline with interpolated event catalogues.
- Explores trade-offs among delta-v, dust mass, and success rate.
Overview
Designing an effective debris remediation constellation requires balancing competing objectives: maximize the fraction of conjunction events that can be feasibly remediated while minimizing total delta-v budgets and required dust mass. This is a challenging multi-objective optimization problem with a complex, nonlinear objective landscape shaped by orbital mechanics and stochastic debris encounters.
I developed a V3 optimization pipeline that uses forward-only propagation and pre-computed event catalogues to enable efficient exploration of the design space. The system supports multiple constellation topologies and uses adaptive evaluation policies to balance accuracy against computational cost.
Design Space
The optimizer works with convenient parameterizations that avoid singularities in orbital elements:
Walker Constellation
Parameters: altitude (km), inclination (°)
Classic Walker-delta/star pattern with configurable satellites per plane. Randomized anomalies avoid singular gradients.
Flower Constellation
Parameters: scale, eccentricity, inclination, ω, Ω, M
6D harmonic flower patterns with altitude derived as a = s·RE + RE + 160 km. Perigee guard ensures a(1−e) ≥ RE + 200 km.
Dual Walker
Parameters: alt₁, alt₂, inc₁, inc₂
Two Walker-like shells at different altitudes and inclinations for improved coverage diversity.
Evaluation Pipeline
The V3 pipeline achieves fast evaluation through several key optimizations that enable evolutionary algorithms to explore thousands of candidate designs:
- Interpolated Event Catalogues: Target states are pre-sampled into state tables and interpolated at runtime, eliminating expensive repeated propagation
- Forward-Only Propagation: Constellation satellites are propagated once per event to an intercept epoch late in the response timeline (default: 2 hours before conjunction). The minimum lead time constraint below governs how much warning is required before that intercept; the intercept epoch itself is the final approach point
- Rust Batch Evaluator: Native backend supports fast batch evaluation with vectorized processing
- Adaptive Policies: BetaPolicy uses credible interval convergence to stop evaluation early when success rate is confidently estimated
Objectives & Constraints
Total Delta-V
Sum of deployment and phasing maneuver costs
Dust Mass
Required mass for momentum transfer
Success Rate
Fraction of events with feasible remediation
Subject to: max deployment Δv ≤ 0.5 km/s, max phasing Δv ≤ 0.1 km/s, minimum lead time ≥ 20 hours, perigee radius ≥ RE + 200 km
Key Results
The optimizer produces Pareto fronts that are being used to explore trade-offs across the design space. Early runs suggest lower-altitude constellations tend to require less delta-v while reaching fewer events, with higher-altitude designs trading increased fuel for broader reach. Characterizing these trends is ongoing work.