SPACE Framework for Space Exploration

• SPACE Framework is a comprehensive methodology that integrates mathematical, algorithmic, and computational approaches for designing and optimizing space exploration infrastructure.
• It employs a dynamic mixed-integer linear programming model coupled with a cooperative game-theoretic decision layer to coordinate public and private sector roles.
• The framework delivers significant cost reduction and operational flexibility, demonstrated by a lunar habitat case study with a computational gap of less than 3%.

The SPACE ("Space Exploration Architecture and Design") Framework encompasses a set of mathematical, algorithmic, and computational methodologies for the design, optimization, and commercialization of space exploration infrastructures. The framework is characterized by its integration of multi-commodity space logistics network modeling, infrastructure subsystem and ISRU (In-Situ Resource Utilization) analysis, and game-theoretic decision mechanisms to allocate tasks and incentives between governmental and commercial players. While its central provenance is in campaign-level lunar and planetary resource logistics and commercial support agreements, its methodology is broadly extensible to space mission planning and infrastructure co-design for a wide array of domains (Chen et al., 2021, Chen et al., 2019).

1. Framework Structure and Scope

The SPACE Framework is grounded in a time-expanded, directed, multi-commodity flow model, where nodes correspond to space locations (Earth surface, LEO, lunar surface, etc.) and arcs denote transportation or operational activities over discretized campaign time steps. This approach enables the explicit co-optimization of subsystem sizing, scheduling, transport, and storage for all commodities relevant to exploration architectures—propellants, crew consumables, ISRU plant masses, power, and spares (Chen et al., 2019).

The framework couples this network flow foundation to a cooperative game-theoretic model, wherein a government space agency (coordinator) interacts with one or more profit-motivated commercial players. Two decision variable classes define the assignment of exploration tasks:

• Participation coefficients $a = (a_1, \dots, a_K)$: the fraction of total demand $D$ assigned to commercial player $k$;
• Incentive coefficients $\theta = (\theta_1,\dots,\theta_K)$: per-kg subsidies paid by the coordinator to each player.

The framework targets both cost reduction and sustainability by optimally distributing infrastructure development, transport, and maintenance duties between the public and private sectors—subject to competitive equilibrium constraints (Chen et al., 2021).

2. Multi-Commodity Logistics and Infrastructure Co-Design

The logistics optimization core of SPACE is formulated as a dynamic, time-expanded mixed-integer linear program (MILP), modeling campaign-level transport and infrastructure deployment. The MILP variables include continuous flows (e.g., mass of O$_2$, H$_2$, and water transported per arc), as well as discrete assets (e.g., vehicle or subsystem counts). Transformation matrices encode vehicle propulsion, infrastructure resource conversion (e.g., yield scaling for ISRU plants), and subsystem synergies (Chen et al., 2019).

Key constraints include:

• Mass and flow conservation for each commodity at each node/time;
• Transformation constraints for ISRU and subsystems: e.g., mapping inputs (regolith, power) to outputs (O$_2$, H$_2$);
• Vehicle, power, and storage capacities limiting the feasible flows on arcs;
• Mission-time windows and operational concurrency;
• Nonnegativity and integrality for all physically realizable variables.

A critical feature is the commodity-packing (multi-fidelity approximation) algorithm, which clusters commodities with identical cost and capacity terms to drastically reduce the computational size of the MILP while preserving solution accuracy below a 3% gap. This allows for systematic "what-if" trade studies across ISRU designs, scheduling granularity, and subsystem coupling (Chen et al., 2019).

3. Cooperative Game-Theoretic Decision Layer

Overlaying the logistics optimization, the SPACE Framework formalizes commercial coordination as a Nash bargaining problem, with explicit utility functions for both the government coordinator and each commercial firm. The key elements are:

• Coordinator utility: $$u_0(a,\theta) = Q - J_0((1-\sum_k a_k) D) - \sum_k \theta_k a_k D$$, where $Q$ is the standalone baseline cost for delivering all demand; $J_0$ and $J_{p,k}$ are fully optimized cost functions for the coordinator and player $k$ respectively.
• Firm utility: $$u_k(a_k, \theta_k) = \theta_k a_k D - J_{p,k}(a_k D)$$.
• Feasibility: Constraints are imposed to ensure $u_z \geq 0 \ \forall z$, thus guaranteeing nonnegative profit for all firms and cost improvement for the coordinator.
• Equilibrium: The system seeks a Nash Bargaining Solution (NBS) maximizing the Nash product $\prod_{z\in Z} u_z(a, \theta)$ or, equivalently (when feasible), the social surplus $U(a) = u_0 + \sum_k u_k$.

Analytical expressions for optimal incentives $\theta^*_k$ as functions of $a^*_k$ provide closed-form allocation rules at the NBS. Three scenario variants allow for joint optimization, fixed allocation with variable incentives, or vice versa (see table below) (Chen et al., 2021).

Scenario	Decision Variables	Optimization Objective
1. Global $(a, \theta)$ design	$a$, $\theta$	Max Nash product or total surplus
2. Fixed $a$, optimize $\theta$	$\theta$ only	Max Nash product with fixed task allocation
3. Fixed $\theta$, optimize $a$	$a$ only	Max total surplus or Nash product at fixed incentive

A central result is that the feasible region for commercial participation and subsidy broadens as ISRU performance increases, and total surplus expands, directly influencing the range of viable public-private architectures.

4. Influence of Demand and Technology Performance

The assignment of payload delivery or infrastructure deployment between coordinator and commercial players is highly sensitive to total demand $D$ and ISRU system characteristics:

• As $D$ increases: The feasible share for any single provider shrinks, necessitating greater collaboration or outsourcing when $D$ exceeds any individual transport capacity.
• For modest $D$: Full commercial outsourcing may be optimal if commercial cost plus required subsidy is less than the baseline coordinator-only cost.
• ISRU productivity: Larger or more efficient lunar-surface ISRU plants ($J_{p,k}$ decreases with ISRU scale) directly expand the range over which firms can profitably participate and the coordinator can justify higher subsidies, increasing robustness and mission flexibility (Chen et al., 2021).

5. Case Study: Lunar Habitat Infrastructure Campaign

A prototypical case paper demonstrates the framework:

1. Network Definition: Nodes representing Earth surface, LEO, EML1, lunar surface; arcs for all relevant transport and holdover operations; 1-day temporal granularity.
2. Parameterization: Annual payload demand $D=30{,}000$ kg, fixed spacecraft and ISRU parameters, launch and operations cost coefficients.
3. Stakeholder Modeling: Coordinator's baseline cost $Q=\$2.058$$B, one commercial player with 10 MT pre-deployed ISRU.</li> <li><strong>Optimization</strong>: MILP solution yields$$a^*=1$(full outsourcing), computed$\theta^*$, and cost outcomes: coordinator expense$< Q$, player profit$>0$$.</li> <li><strong>Sensitivity</strong>: Examination of results as ISRU productivity, launch cadence, and storage sizing vary.</li> </ol> <p>This systematic process validates both the modeling tractability and the incentive structure prescribed by the SPACE framework (<a href="/papers/2103.08970" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Chen et al., 2021</a>, <a href="/papers/1910.04265" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Chen et al., 2019</a>).</p> <h2 class='paper-heading' id='extensions-and-generalizations'>6. Extensions and Generalizations</h2> <p>Numerous extensions have been developed or proposed:</p> <ul> <li><strong>Multiple Commercial Players</strong>: Nash bargaining generalizes to$$K+1$$players, or sequential subgames for prioritized allocations.</li> <li><strong>Heterogeneous Platforms</strong>: Distinct ISRU types, propulsion options, and mission specialties are modeled via commodity- and arc-specific cost/constraint matrices.</li> <li><strong>Uncertainty and Robustness</strong>: Stochastic or chance-constrained optimization in$$J_0$and$J_{p,k}$$, accommodating risk and parametric uncertainty.</li> <li><strong>Temporal Dynamics</strong>: Participation and incentive coefficients$$(a_k(t), \theta_k(t))$$can vary across distinct campaign phases with periodic time-expanded networks, addressing infrastructure buildup versus steady-state operations.</li> <li><strong>Alternate Bargaining Solutions</strong>: Kalai–Smorodinsky or weighted Nash products enable policy-driven reward floors or differential firm prioritization.</li> <li><strong>New Domains</strong>: The framework is adaptable for Mars logistics, on-orbit servicing, or propellant depots, given redefined baseline costs, commodity-sets, and network topologies (<a href="/papers/2103.08970" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Chen et al., 2021</a>).</li> </ul> <h2 class='paper-heading' id='practical-guidelines-and-computational-performance'>7. Practical Guidelines and Computational Performance</h2> <p>The framework’s scalability and efficacy are supported by:</p> <ul> <li><strong>Commodity packing</strong>: Acceleration of MILP solution times by$$60–95\%$with sub-$3\%$$gap versus full-size formulation;</li> <li><strong>Subsystem coupling</strong>: Power, storage, and ISRU synergies yield$$30–40\%$ campaign Initial Mass in LEO (IMLEO) savings over “black-box” planning;
4. Rapid trade studies: Enables high-fidelity, multi-scenario analysis including storage-transport trade-offs, launch schedule co-design, and infrastructure sizing with integrated subsystem technology models.

These capabilities delineate SPACE as a practical and extensible decision-support machinery for sustainable, mutually beneficial government–industry collaboration in space exploration (Chen et al., 2019).

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The SPACE Framework constitutes an integrated, optimization- and game-theoretic paradigm for commercialized space exploration architecture, aligning systemic logistics, infrastructure technology, and incentive-compatible stakeholder participation (Chen et al., 2021, Chen et al., 2019).