Stochastic Multistage Constellation Reconfiguration Problem: Stochastic Dual Dynamic Integer Programming Approach

This paper extends the Multistage Constellation Reconfiguration Problem (MCRP) into the Stochastic MCRP (SMCRP), incorporating stochastic target properties through the use of Stochastic Dual Dynamic Integer Programming (SDDiP) and developing the SDDiP algorithm alongside additional solution methods. The SDDiP algorithm presented determines the optimal policy of orbital maneuvers within an array of stochastic scenarios with realizations of uncertain mission parameters, including target visibility and rewards. Due to the nature of SDDiP, the SDDiP algorithm converges to global optimality within finite iterations, certifying that the orbital maneuver sequence of each scenario obtains the maximum observation rewards. The SMCRP is additionally modeled as a Markov decision process, which is then solved through the use of value iteration and Q-Learning for comparative purposes within two computational experiments.

The computational experiments conducted in Sec. IV demonstrate the capability of the SDDiP algorithm to obtain optimal orbital maneuvering sequences under various uncertain parameter conditions for different mission purposes. Within the experiment concerning orbital targets and observation satellites in LEO, the policy obtained by the SDDiP algorithm outperforms all other SMCRP solution methods, especially relative to the non-maneuverable constellation and random maneuver policy. Additionally, the SDDiP algorithm policy performance closely mirrors the deterministic upper bound MCRP solution in a majority of scenarios. Similarly, within the experiment concerning hurricanes, the policy obtained by the SDDiP algorithm obtains identical rewards to the MCRP solution in all scenarios under realistically simulated random hurricane trajectories. Both experiments demonstrate the performance of the SDDiP algorithm above other SMCRP solution methods under various conditions, obeying orbital maneuver feasibility and physical VTW constraints while accounting for uncertain target motion and rewards. Overall, the SDDiP algorithm provides robust orbital maneuver decisions under uncertainty, presenting itself as a valuable stochastic algorithm while leveraging the multistage reconfiguration methodology of the MCRP.

Future efforts to improve the optimization of orbital maneuverability under uncertain target conditions may progress in a myriad of directions. A priority would be to devise a new reformulation of the SMCRP such that the overall mission budget parameter c max from constraints (1d) may be included in both the SDDiP algorithm and MDP formulations for a solution that may take any general orbital slots as input. Similarly, larger test instances composed of more scenarios and more targets in each scenario would further exemplify the effectiveness of the SDDiP algorithm under a much larger set of uncertainty. Finally, an extension of the MCRP for the EOSSP is the REOSSP in Ref. [10], so a logical extension of the SMCRP would be to incorporate other aspects of satellite scheduling also under target uncertainty, performing full operations of data downlink to ground station and solar charging with stochasticity.

Improvements to AI Systems:

1. Stochastic Multistage Decision-Making with Finite-Time Optimality Guarantees: Implement the SDDiP algorithm as a core planning module for AI systems that must make sequential decisions under uncertainty (e.g., autonomous satellite constellations, drone fleets, or robotic exploration). The AI system can now compute globally optimal action sequences over a finite horizon, with certified convergence, even when rewards and state transitions are stochastic—unlike typical reinforcement learning (RL) approaches that lack optimality certificates.

2. Hybrid MDP + SDDiP Policy Selection: Build an AI controller that dynamically switches between value iteration, Q-Learning, and SDDiP based on problem size and available computational budget. The system can use SDDiP for small-to-medium instances to guarantee optimality, and fall back to Q-Learning for larger, real-time scenarios, while using value iteration as a baseline for verification. This yields an AI that balances optimality, speed, and scalability.

3. Uncertainty-Aware Reward Maximization with Physical Constraint Satisfaction: Enhance AI planning systems to explicitly incorporate hard physical constraints (e.g., orbital maneuver feasibility, VTW windows) alongside stochastic rewards. The improved AI can generate action sequences that are provably feasible in every scenario, avoiding infeasible plans that RL agents often produce when trained solely on reward maximization.

4. Scenario-Robust Policy Generalization: Use the SDDiP-derived policies as training data or expert demonstrations for imitation learning in RL agents. The AI system can learn a policy that mimics the optimal stochastic decisions across thousands of scenarios, enabling fast inference in new, unseen uncertainty realizations—achieving near-deterministic-upper-bound performance without needing to re-solve the stochastic program each time.

5. Budget-Constrained Stochastic Planning (Future Extension): Although not yet implemented, the paper’s identified gap (excluding budget constraint c) suggests an AI system can be designed to accept a mission budget as an input and produce Pareto-optimal trade-offs between reward and fuel/energy cost. The improved system would solve a constrained SMCRP, outputting a set of maneuver policies that maximize expected reward per unit of budget, useful for long-duration autonomous missions.

6. Multi-Objective Satellite Scheduling under Uncertainty: Extend the AI system to jointly optimize observation, data downlink, and solar charging under stochastic target motion (as the paper suggests for REOSSP). The improved system would generate full operational schedules (not just maneuvers) that are robust to weather, target drift, and power fluctuations, using SDDiP’s finite-time convergence to certify performance in each scenario.

What the Improved AI System Can Do:

• Autonomous Constellation Management: Given a set of LEO satellites and uncertain targets (e.g., moving ships, storms), the AI can compute, in real time, the optimal reconfiguration maneuvers to maximize total observation reward, with a mathematical guarantee of optimality within a finite number of iterations, while respecting all orbital mechanics and visibility constraints.

• Disaster Response Planning: For hurricane tracking, the AI can generate maneuver sequences that yield identical rewards to the deterministic optimal solution across all simulated storm trajectories, enabling reliable, pre-computed response plans that adapt to evolving forecasts.

• Resource-Constrained Autonomous Operations: When a mission budget is added, the AI can produce a set of candidate policies, each optimized for a different budget level, allowing operators to select the best trade-off between scientific return and fuel expenditure.

• Benchmarking and Verification Tool: The AI can serve as a gold-standard solver to validate other RL or heuristic methods, providing upper-bound performance estimates and identifying where approximate methods lose optimality in stochastic settings.