Preface: Why Is This Necessary?
Deep space exploration and long-duration interplanetary expeditions (e.g., Mars Mission, Artemis) present humanity with an unprecedented challenge: a management deficit. With signal latencies ranging from 20 to 40 minutes, the traditional hierarchical "Center-to-Executive" model becomes critically vulnerable. Any delay in decision-making during emergency scenarios leads to a cascading increase in entropy and the potential loss of the mission.
Adaptive Autonomy Balance (AAB) is the solution to the requirement for self-organizing systems. It is not merely a delegation of authority, but a mathematically grounded mechanism for the dynamic allocation of control. It transforms an isolated crew from an "object of management" into an "autonomous subject," maintaining structural integrity without constant communication with Earth.
The Adaptive Autonomy Balance (AAB) Concept
AAB is an engineering modeling framework for the dynamic allocation of autonomy between humans and automated systems. The framework functions as a closed-loop regulator, adjusting the system's degree of self-governance in response to measured workload, resilience indicators, and network connectivity.
Mathematical Model of Resilience
At the core of AAB lies a modified logistic equation describing the dynamics of resilience $R(t)$ considering the autonomy weight $A$:
$$\frac{dR}{dt} = r \cdot R \cdot \left(1 - \frac{R}{K}\right) - d \cdot R + a \cdot A \cdot \left(1 - \frac{R}{K}\right)$$
System Parameters:
$R$: Resilience (the current state of the system).
$r$: Resilience growth rate (0.05).
$K$: Carrying capacity/System limit (1.0).
$d$: Decay/Degradation rate (0.02).
$a$: Autonomy influence coefficient (0.1).
$A$: Autonomy weight $[0, 1]$ relative to central command ($C=1$).
The autonomy term is bounded by the factor $(1 - R/K)$, ensuring the system remains within physical constraints and maintaining the engineering rigor of the model.
Critical Metrics:
Inflection Point (A ≈ 0.6): The engineering optimum. At this value, a significant increase in resilience (+35.6%) is achieved while maintaining a low level of group entropy (uncertainty). This represents the "safe zone" for critical decision-making in isolation.
Percolation Threshold: To prevent the disintegration of the group structure under full autonomy, a critical mass of resource support is required (index ≈ 9.00 per crew member). Below this threshold, entropy grows exponentially, leading to system disintegration.
Conclusion
The AAB framework demonstrates that non-linear autonomy weighting transforms natural system decay into adaptive growth. Implementing real-time AAB-based
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