Resilience Map

Definition

The Resilience Map is an SSA architecture evaluation visualization tool proposed by Klonowski (2025). It presents a heatmap showing a given SSA architecture's detection capability over time for low-thrust spacecraft starting from any initial position in cislunar space. The Resilience Map captures the dynamic evolution characteristics of SSA architecture coverage, serving as an important complement to traditional static volume coverage ratio metrics.

Generation Method

Step 1: Precompute Reachable Sets

Precompute the reachable sets of low-thrust spacecraft on a three-dimensional grid in cislunar space:

  • Grid Resolution: Covers critical regions of cislunar space
  • Time Horizon: Evaluation period (e.g., 7 days)
  • Control Constraint: Low-thrust upper bound

Step 2: Coverage Overlay

For each grid point and each time step:

  • Check whether the reachable set at that point intersects the architecture's detection region
  • Calculate the fraction of the reachable set that is detected

Step 3: Heatmap Generation

Visualize the coverage analysis results:

  • Color Encoding: Red indicates high coverage capability, blue indicates low coverage capability
  • Time Dimension: Animation showing how coverage evolves over time
  • Spatial Dimension: Two-dimensional slices or three-dimensional volume rendering

Comparison with Traditional Volume Coverage Ratio

MetricDescriptionLimitations
Volume Coverage RatioFraction of static points within the architecture's detection regionCannot reflect dynamic target detection capability
Resilience MapTemporal match between reachable sets and detection regionsHigher computational cost

Core Elements

Mathematical Definition

The Resilience Map RM(x0,t)\mathcal{RM}(\mathbf{x}_0, t) is defined as the fraction of the low-thrust reachable set Rt(x0)\mathcal{R}^t(\mathbf{x}_0) from initial position x0\mathbf{x}_0 that is detected by the architecture at time tt:

RM(x0,t)=Vol(Rt(x0)∩D(t))Vol(Rt(x0))\mathcal{RM}(\mathbf{x}_0, t) = \frac{\text{Vol}(\mathcal{R}^t(\mathbf{x}_0) \cap \mathcal{D}(t))}{\text{Vol}(\mathcal{R}^t(\mathbf{x}_0))}

where D(t)\mathcal{D}(t) is the detection region at time tt.

Key Properties

The Resilience Map can:

  • Identify temporal blind spots in architecture coverage
  • Quantify the architecture's detection capability for dynamic targets
  • Provide localized improvement directions for architecture optimization

Application Scenarios

The Resilience Map is applicable to SSA architecture performance evaluation, resource allocation optimization, and mission planning scenarios.

References

  • Klonowski M, Holzinger M J. Resilience of Architectures for Cislunar Space Situational Awareness Using Low-Thrust Reachable Sets[J]. The Journal of Spacecraft and Rockets, 2025.
  • Klonowski M. Cislunar Space Situational Awareness Architecture Design and Analysis[D]. University of Colorado Boulder, 2025.