Spacecraft Fiducial Marker for Autonomous Rendezvous, Proximity Operations, and Docking

Technical Summary: AstraTag – A Recursive Fiducial Marker for Autonomous On-Orbit Robotics

Problem Statement
Autonomous robotic operations in space, including Rendezvous, Proximity Operations, and Docking (RPOD), are critical for missions such as In-Space Assembly and Manufacturing (ISAM), On-Orbit Servicing (OOS), and Active Debris Removal (ADR). These operations require accurate relative state estimation between a chaser and a target spacecraft. While fiducial markers provide robust visual references for pose estimation, existing solutions (e.g., standard ArUco, AprilTag) are largely designed for terrestrial robotics and single-scale detection. A significant limitation arises during close-range proximity and docking: as the camera approaches the target, the marker often exceeds the camera's field of view or becomes too large to resolve fully, leading to a loss of tracking precisely when it is most needed. Furthermore, standard markers struggle on the curved, non-planar surfaces common to spacecraft buses and modules, where perspective distortion degrades detection reliability.

Methodology: The AstraTag Design
The paper proposes AstraTag, a recursive fiducial marker specifically engineered for on-orbit robotic operations. Its design and detection pipeline address the challenges of multi-scale detection and curved surface distortion through the following mechanisms:

• Recursive Spidron Structure: The marker template is based on a square Spidron pattern, a self-similar fractal composed of alternating triangles. The design features a square outer boundary for standard perspective-n-point (PnP) pose estimation. Inside this boundary, the encoding pattern is replicated at a reduced scale at the center. This recursive structure allows the marker to be detected at long ranges (via the outer layer) and at close ranges (via the inner, smaller layer) when the outer layer leaves the field of view.
• Encoding Scheme: Each of the eight triangular regions of the Spidron is subdivided into six smaller triangles using seven control points (vertices, edge midpoints, and an approximate centroid). This yields 48 encoding cells. The binary signature derived from these cells is protected by a Generalised Reed–Solomon (GRS) code, providing error correction against local image degradation, partial occlusion, and imperfect binarization.
• Detection Pipeline:
  1. Preprocessing: Images undergo Contrast-Limited Adaptive Histogram Equalization (CLAHE) and adaptive Gaussian thresholding to handle uneven illumination.
  2. Quadrilateral Localization: Contours are extracted and analyzed using the Probabilistic Hough Transform to identify valid quadrilaterals. The pipeline validates candidates based on parallel side pairs and refines corners to sub-pixel accuracy.
  3. Signature Matching: A perspective homography normalizes the detected region. The signature is extracted via area-based sampling of the triangular cells and matched against a pre-computed dictionary using Hamming distance.
  4. Curved Surface Fallback: For markers on non-planar surfaces, the system employs a Thin-Plate Spline (TPS) re-warp fallback. This utilizes the marker's internal white rectangular borders as additional geometric correspondences to correct non-linear distortions caused by curvature.
• Pose Estimation: The system uses Infinitesimal Plane-based Pose Estimation (IPPE), an analytical, non-iterative method that solves for the 6-DoF pose (rotation and translation) using the matched 2D-3D corner correspondences.

Key Contributions
The paper outlines four primary contributions:

1. Recursive Marker Design: A novel fiducial marker based on the Spidron fractal pattern, featuring GRS-based encoding and area-based signature sampling to enable detection across varying distances.
2. Multi-Scale Detection Pipeline: A detection system that leverages the recursive structure to maintain tracking from long approach ranges down to close-proximity docking, where single-scale markers fail.
3. Curved Surface Robustness: The integration of a TPS-based unwarping mechanism that uses internal rectangular borders as geometric correspondences, extending reliable detection to 70° out-of-plane rotation on curved surfaces.
4. Comprehensive Benchmarking: A comparative evaluation against Fractal ArUco and AprilTag on both flat and curved spacecraft mockups under simulated space lighting conditions.

Experimental Results
The authors evaluated AstraTag against Fractal ArUco (3-layer) and AprilTag on two datasets: a flat-surface mockup (Aditya-L1 bus) and a curved-surface mockup (cylindrical space station module).

• Curved Surface Performance: On the cylindrical module, AstraTag demonstrated superior robustness. It maintained a detection rate of 97–100% for out-of-plane rotations up to 70°, enabled by the TPS fallback. In contrast, Fractal ArUco detection collapsed to 0% at high rotation angles (40°+), and AprilTag dropped to 56% at 70°.
• Distance Performance: On the curved surface, AstraTag averaged an 87.2% detection rate across distances, while Fractal ArUco averaged only 21.9% due to the inability to resolve inner fractal layers under curvature distortion. AprilTag achieved 100% detection across distances but required a significantly larger physical print area (2.76× the area of AstraTag for the same nominal tag size) to achieve this.
• Flat Surface Performance: On the flat Aditya-L1 mockup, all three markers achieved near-perfect detection (AstraTag and AprilTag at 100%, Fractal ArUco at 99.3%), confirming that surface curvature is the primary differentiator in performance gaps.
• Material Durability: The paper notes that AstraTag was successfully printed on Metalphoto anodized aluminum, a material capable of withstanding extreme temperatures and UV radiation, with 100% detection and identification rates across the tested range.

Significance and Claims
The paper positions AstraTag as a robust, recursive-marker option specifically tailored for the constraints of space robotics. The authors claim that the marker addresses the critical gap in existing fiducial systems where reliable tracking is lost during the final proximity and docking phases due to field-of-view limitations and surface curvature. By combining a self-similar fractal design with geometric correction for curved surfaces, AstraTag offers a scalable solution for large constellations and cooperative docking scenarios. The authors emphasize that while the current implementation relies on dictionary matching, the underlying GRS encoding allows for future algebraic decoding, further enhancing efficiency. The work contributes to the standardization efforts for on-orbit servicing by providing a marker design that is resilient to the perceptual challenges of the space environment, including high contrast, reflections, and non-planar geometries.