Adjustable AprilTags: Adaptive Fiducial Systems

• Adjustable AprilTags are fiducial systems that intentionally vary marker parameters—such as pose, layout, and payload—to enhance performance in non-ideal conditions.
• They employ techniques like stochastic pose adjustment, family-level redesign, recursive multi-scale geometry, and detector-side calibration to improve tracking and localization.
• Practical implementations demonstrate improved accuracy, robustness against installation errors, and dynamic adaptability for applications ranging from robotics to security.

Adjustable AprilTags are AprilTag-based fiducials or AprilTag-centered pipelines in which some aspect of the marker system is intentionally varied to preserve performance under non-ideal operating conditions. In the cited literature, that variation appears in several distinct forms: stochastic adjustment of a tag’s assumed pose in localization, family- or layout-level redesign to trade memory, ambiguity, and detection behavior, recursive multi-scale geometry for close-range continuity and curved-surface robustness, electronically changeable payloads for identity security, physically non-coplanar dynamic tag assemblies for reflective environments, and detector-side adaptation for highly distorted optics (Kayhani et al., 2022, Springer et al., 2022, Thakur et al., 25 Jun 2026, Li, 17 Aug 2025, Mateos, 2020, Duisterhof et al., 2022). The common theme is not a single marker design, but controlled modification of the tag, its model, or its decoding process so that a fixed AprilTag assumption is replaced by an explicitly parameterized one.

1. Conceptual scope

The phrase “adjustable AprilTags” does not denote a single canonical construction. In construction robotics, adjustability is algorithmic: the tag is physically fixed, but its uncertain installation is modeled on $\mathrm{SE}(3)$ so that the estimator can soften the contribution of a likely misplaced landmark (Kayhani et al., 2022). In embedded landing systems, adjustability can mean choosing a different AprilTag family or layout, such as comparing the default AprilTag 48h12 against a custom 24h10 family, with consequences for RAM, detection rate, and orientation ambiguity (Springer et al., 2022). In spacecraft RPOD, the relevant adjustment is geometric and multi-scale: recursive layers and internal borders are used so that some resolvable portion of the fiducial remains usable as the camera moves from long range to docking range or observes the tag on a curved surface (Thakur et al., 25 Jun 2026).

A different line of work uses “adjustable” literally. The note on identity-secured tasks defines Adjustable AprilTags as square fiducials whose identity-encoded internal black-white cell matrix is not fixed in print but can be changed dynamically by the legitimate entity, for example on an electronic display synchronized with roadside units (Li, 17 Aug 2025). AprilTags3D extends this literal sense further: tags displayed on LCD screens can change ID at runtime while remaining part of a rigid, physically 3D tag assembly whose non-coplanar faces stabilize pose estimation in glare-heavy RGB-only environments (Mateos, 2020).

Detector-side adjustment is another distinct meaning. TartanCalib does not redefine the tag payload, but iteratively adapts AprilTag detection and subpixel refinement using an intermediate wide-angle camera model, virtual pinhole views, distortion-aware reprojection, and adaptive refinement windows (Duisterhof et al., 2022). A plausible implication is that, across these works, adjustability is best understood as a systems property: the marker, its pose prior, its codebook, its geometry, and its detector may all be made conditional on operating context rather than treated as immutable.

2. Stochastic adjustability on the pose manifold

In tag-based visual-inertial localization for indoor construction, the central problem is that AprilTags are manually installed and therefore subject to installation error in 6-DoF pose relative to the inertial frame. The cited work models each tag pose as a nominal mean pose plus a zero-mean Gaussian perturbation in the tangent space of $\mathrm{SE}(3)$ (Kayhani et al., 2022):

$$T_{I\!T_j} = \exp(\hat{\xi}_j)\,\bar{T}_{I\!T_j}, \qquad \xi_j \sim \mathcal{N}(0,\Sigma_T).$$

The camera-body state is $X_k \equiv T_{I\!B_k} \in \mathrm{SE}(3)$, with a fixed calibrated body-to-camera transform $T_{B\!C}$. Tag corner measurements are formed by projecting known tag-frame corners through the camera model, then linearizing both the perturbed tag pose and the projection. For the stacked corners of tag $j$ at time $k$, the residual is

$$r_k^{(j)} \approx H_X\,\delta x_k + H_T\,\xi_j + \nu_k^{(j)},$$

with residual covariance

$$\Sigma_r \approx H_T\,\Sigma_T\,H_T^\top + R_{\text{pix}}.$$

This is the paper’s core notion of adjustability: as $\Sigma_T$ increases, the residual covariance grows, and the estimator automatically down-weights measurements from tags that are likely to be misplaced (Kayhani et al., 2022). The tags themselves are unchanged; what changes is the estimator’s confidence in them.

The formulation is integrated into an on-manifold EKF, denoted TIE-EKF. Prediction uses the nominal body motion $\mathrm{SE}(3)$0 and the adjoint $\mathrm{SE}(3)$1 for perturbation propagation. Measurement update is tightly coupled at the corner level, with block-diagonal measurement covariance augmented by the mapped tag-pose uncertainty. Correction uses on-manifold retraction: $\mathrm{SE}(3)$2 (Kayhani et al., 2022).

The reported experiments use a Parrot Bebop 2 with monocular camera and IMU, three AprilTags of size $\mathrm{SE}(3)$3 m, and trajectories planned so that at least one tag is always visible. Four uncertainty cases are evaluated with 200 Monte Carlo runs each: single-low, single-high, all-low, and all-high. Across simulation and lab experiments, TIE-EKF consistently reduced the median, maximum, and spread of RMSE relative to a baseline EKF, with typical accuracy improvements of $\mathrm{SE}(3)$4–$\mathrm{SE}(3)$5 depending on scenario. In an extreme 3DC robustness test with all tags heavily perturbed and 400 runs, the baseline EKF exhibited divergence, with many runs having RMSE $\mathrm{SE}(3)$6 m, whereas TIE-EKF maintained bounded errors with median and mode close to zero and significantly fewer divergences (Kayhani et al., 2022).

The practical tuning rules are explicit. Isotropic priors use $\mathrm{SE}(3)$7, while anisotropic priors can inflate translation along the wall normal and rotation about the wall normal when tags are placed on planar walls. Strong priors make tags “stiff”; weak priors make them “soft.” The paper also gives example covariances for wall-parallel tags and for typical human placement quality of $\mathrm{SE}(3)$8 mm translational and $\mathrm{SE}(3)$9–$$T_{I\!T_j} = \exp(\hat{\xi}_j)\,\bar{T}_{I\!T_j}, \qquad \xi_j \sim \mathcal{N}(0,\Sigma_T).$$0 rotational uncertainty (Kayhani et al., 2022). A common misconception is that robust tag-based localization requires physically re-surveying every misplaced marker. This work directly argues the opposite: algorithmic adjustability can compensate for predictable installation uncertainty without physically altering the tag field.

3. Family- and layout-level adjustment, ambiguity, and embedded constraints

A different form of adjustability operates at the tag-family level. The landing-oriented evaluation of AprilTag and WhyCode compares the default AprilTag 48h12 to a custom AprilTag 24h10 designed to preserve embeddability while reducing memory demands on embedded hardware (Springer et al., 2022). AprilTag 48h12 has 4 undefined center squares, 20 white-border squares, 28 black-border squares, and 48 data-bit squares, totaling 96 defined squares. The custom 24h10 reduces the undefined center to one square and uses 8 white-border squares, 16 black-border squares, and 24 data-bit squares, totaling 48 defined squares. The design consequence is a drastic reduction in family size: 24h10 has only 18 markers, whereas 48h12 has 42,211 markers and can exceed 1 GB of RAM (Springer et al., 2022).

The empirical result is cautionary. AprilTag 24h10 did not improve detection rate over 48h12, and it exhibited a higher discontinuity rate $$T_{I\!T_j} = \exp(\hat{\xi}_j)\,\bar{T}_{I\!T_j}, \qquad \xi_j \sim \mathcal{N}(0,\Sigma_T).$$1 than 48h12, indicating worse orientation stability in monocular pose estimation (Springer et al., 2022). The paper defines orientation ambiguity as unreliability of planar marker orientation estimates from a monocular single image when some viewpoints produce indistinguishable appearances. It quantifies discontinuities using simultaneous linear and angular criteria:

$$T_{I\!T_j} = \exp(\hat{\xi}_j)\,\bar{T}_{I\!T_j}, \qquad \xi_j \sim \mathcal{N}(0,\Sigma_T).$$2

$$T_{I\!T_j} = \exp(\hat{\xi}_j)\,\bar{T}_{I\!T_j}, \qquad \xi_j \sim \mathcal{N}(0,\Sigma_T).$$3

and computes

$$T_{I\!T_j} = \exp(\hat{\xi}_j)\,\bar{T}_{I\!T_j}, \qquad \xi_j \sim \mathcal{N}(0,\Sigma_T).$$4

On a Raspberry Pi 4 with 2 GB RAM, using a 480p webcam stream and controlled indoor lighting, both AprilTag families had lower detection rates than WhyCode variants, which the authors attribute to the AprilTag ROS pipeline requiring image transmission to image_proc for rectification and back (Springer et al., 2022). The paper therefore rejects a simple intuition that smaller or more memory-efficient families are automatically better for embedded autonomy.

The same study provides several design implications for adjustable AprilTags in landing. It recommends preferring AprilTag 48h12 over 24h10 for lower orientation ambiguity, maintaining embeddability so that a smaller tag can be embedded for close-in phases, increasing printed tag size to reduce distance-induced ambiguity, preserving high contrast and crisp borders, minimizing pipeline latency, and applying temporal continuity checks or IMU fusion to reject 90°/180°-like flips (Springer et al., 2022). This suggests that family-level adjustment is useful, but only when the trade-off between memory, geometric stability, and downstream controller sensitivity is explicitly managed.

4. Recursive and multi-scale adjustment for proximity and curvature

Single-scale square-grid markers face two symmetric failure modes in RPOD. At long range, interior cells become sub-pixel and can no longer be decoded. At short range, the outer quadrilateral leaves the field of view or is clipped, precisely when continuous tracking is most critical (Thakur et al., 25 Jun 2026). The spacecraft fiducial work addresses this with AstraTag, a recursive square Spidron-based marker whose self-similar structure supports detection across multiple spatial scales. For $$T_{I\!T_j} = \exp(\hat{\xi}_j)\,\bar{T}_{I\!T_j}, \qquad \xi_j \sim \mathcal{N}(0,\Sigma_T).$$5, the nested squares obey

$$T_{I\!T_j} = \exp(\hat{\xi}_j)\,\bar{T}_{I\!T_j}, \qquad \xi_j \sim \mathcal{N}(0,\Sigma_T).$$6

$$T_{I\!T_j} = \exp(\hat{\xi}_j)\,\bar{T}_{I\!T_j}, \qquad \xi_j \sim \mathcal{N}(0,\Sigma_T).$$7

The template uses three concentric layers separated by white rectangular borders. These borders stabilize quadrilateral localization and also provide internal geometric correspondences for a Thin-Plate Spline fallback on curved surfaces. The encoded signature is 48-bit, derived from triangular sub-regions and protected by a Generalised Reed–Solomon code. Detection uses contour-based quadrilateral localization, homography-based perspective normalization, area-based sampling of triangular cells, Hamming-distance matching against a pre-computed dictionary storing all four cyclic orientations, and TPS re-warp when curvature or severe out-of-plane rotation distorts the patch (Thakur et al., 25 Jun 2026). The TPS kernel and warp are

$$T_{I\!T_j} = \exp(\hat{\xi}_j)\,\bar{T}_{I\!T_j}, \qquad \xi_j \sim \mathcal{N}(0,\Sigma_T).$$8

$$T_{I\!T_j} = \exp(\hat{\xi}_j)\,\bar{T}_{I\!T_j}, \qquad \xi_j \sim \mathcal{N}(0,\Sigma_T).$$9

The curved-surface dataset shows the main advantage. AstraTag sustains $X_k \equiv T_{I\!B_k} \in \mathrm{SE}(3)$0–$X_k \equiv T_{I\!B_k} \in \mathrm{SE}(3)$1 detection from $X_k \equiv T_{I\!B_k} \in \mathrm{SE}(3)$2–$X_k \equiv T_{I\!B_k} \in \mathrm{SE}(3)$3 rotation due to the TPS fallback; AprilTag maintains $X_k \equiv T_{I\!B_k} \in \mathrm{SE}(3)$4 to $X_k \equiv T_{I\!B_k} \in \mathrm{SE}(3)$5 and drops to $X_k \equiv T_{I\!B_k} \in \mathrm{SE}(3)$6 at $X_k \equiv T_{I\!B_k} \in \mathrm{SE}(3)$7; Fractal ArUco falls to $X_k \equiv T_{I\!B_k} \in \mathrm{SE}(3)$8 at $X_k \equiv T_{I\!B_k} \in \mathrm{SE}(3)$9 and $T_{B\!C}$0 beyond. At $T_{B\!C}$1, all fail because the quad is not recoverable near edge-on (Thakur et al., 25 Jun 2026). On distance robustness for the curved dataset, AprilTag achieves $T_{B\!C}$2 detection at $T_{B\!C}$3–$T_{B\!C}$4 cm, AstraTag averages $T_{B\!C}$5, and Fractal ArUco averages $T_{B\!C}$6. The paper notes an important normalization caveat: although all tags were specified at $T_{B\!C}$7 cm, the AprilTag layout used, tagCustom48h12, extends data cells beyond the inner quad, yielding a print 1.67× larger per dimension and 2.76× larger area than AstraTag and Fractal ArUco (Thakur et al., 25 Jun 2026). On flat spacecraft-bus data, AstraTag and AprilTag both achieve $T_{B\!C}$8 detection across all conditions.

The paper translates these findings into direct guidance for “Adjustable AprilTags.” It recommends adding recursive or self-similar layers, preserving an outer quad for long range and inner quads for close-range continuity, inserting crisp internal rectangular borders to support TPS control points, distributing payload across sub-regions to improve partial-occlusion tolerance, and adopting stronger ECC such as GRS with configurable $T_{B\!C}$9 and minimum distance $j$0 (Thakur et al., 25 Jun 2026). A plausible implication is that multi-scale adjustability is most valuable when continuous tracking over a wide approach corridor is more important than maximizing conventional AprilTag simplicity.

5. Dynamic payloads, electronic tags, and physically 3D assemblies

The identity-security note gives the most literal definition of Adjustable AprilTags: electronically controllable fiducials whose identity-coded visual pattern can be changed on demand rather than printed once and left immutable (Li, 17 Aug 2025). The adjustable parameters include payload bits, error-correction strength, codebook selection, rotation schedules, ephemeral codes, keyed variants, visual pattern elements, and detector-side thresholds. For a tag length $j$1 and $j$2 information bits, the cited coding-theoretic relations are

$j$3

The note also gives approximate false-identification and decoding-failure expressions under random-background and i.i.d. bit-flip models, and proposes a keyed rolling-code construction in which the payload is derived from $j$4 before ECC encoding (Li, 17 Aug 2025).

The security model is tied to open/public environments, especially vehicle-road cooperation with roadside units. Fixed printed tags are treated as vulnerable to spoofing, cloning, replay, adversarial perturbations, and following attacks. The adjustable countermeasure is synchronized “adjust and capture”: the legitimate agent rotates to a new code from a curated codebook with large pairwise Hamming distances, and the verifier immediately switches to the corresponding active codebook or expected keyed payload. The note preserves the baseline AprilTag 2/3 detection pipeline—thresholding, quad detection, corner refinement, homography estimation, cell binarization, codeword decoding, and ID lookup—but adds synchronization, adjustable thresholds, dynamic codebook lookup, and confidence-based acceptance or rejection (Li, 17 Aug 2025). It explicitly states that it does not report quantitative metrics, although it frames evaluation in terms of TPR, FAR, FRR, and EER.

AprilTags3D addresses a different operational problem: robust pose estimation and indirect communication in highly reflective environments using dynamic LCD-displayed tags mounted on different planes (Mateos, 2020). Here, “adjustable” refers both to dynamic IDs and to physical orientation. Tags are rendered on LCD screens, their content can change without sacrificing pose continuity, and the screens are rotated with respect to one another so that at least one tag remains well observed under glare. Individual tag poses are estimated in the standard planar way, then fused subject to known rigid transforms between tags. The consistency objective is written on $j$5 as

$j$6

with confidence weights derived from distance and orientation heuristics (Mateos, 2020). The paper emphasizes that pose estimation is tied to corners and known tag size rather than to the ID, so changing the ID does not affect pose so long as border and geometry remain constant.

The reported results are substantial. Indoors, classic AprilTags achieved $j$7 detection with yaw error about $j$8, whereas AprilTags3D with two dynamic markers and a follower rotated $j$9 achieved $k$0 detection and yaw error $k$1. Outdoors in strong sun and water glare, classic AprilTags achieved $k$2 detection with yaw error about $k$3 and required on average five attempts before successful latching; AprilTags3D achieved $k$4 detection and yaw error $k$5 (Mateos, 2020). These results show that dynamic adjustability can be geometric as much as informational: changing the payload secures communication, while changing the physical view geometry stabilizes pose.

6. Detector-side adaptation, alternative fiducials, and cross-cutting trade-offs

TartanCalib shows that adjustability may reside entirely in the detector-calibration loop rather than in the fiducial’s codebook or physical layout (Duisterhof et al., 2022). The system iteratively detects an AprilTag board, estimates the target pose, builds an intermediate camera model, and then uses that model to adjust detection and refinement through three mechanisms: undistorting the image into virtual pinhole cameras, reprojecting the calibration target into the distorted image, and adaptive subpixel refinement of AprilTag corners. Calibration minimizes

$k$6

The adaptive corner-refinement window is scaled by local projected tag spacing, and the full procedure typically converges in 2–3 iterations (Duisterhof et al., 2022). Quantitatively, combining adaptive subpixel refinement and feature reprojection improves reprojection errors by up to $k$7, helps detect up to $k$8 more features, and improves downstream dense depth mapping. On ultra-wide Lensagon BF5M datasets, virtual pinhole undistortion adds another $k$9–$$r_k^{(j)} \approx H_X\,\delta x_k + H_T\,\xi_j + \nu_k^{(j)},$$0 features, and normalized detection in periphery bins improves to $$r_k^{(j)} \approx H_X\,\delta x_k + H_T\,\xi_j + \nu_k^{(j)},$$1 across all angles where competing detectors dropped as low as $$r_k^{(j)} \approx H_X\,\delta x_k + H_T\,\xi_j + \nu_k^{(j)},$$2–$$r_k^{(j)} \approx H_X\,\delta x_k + H_T\,\xi_j + \nu_k^{(j)},$$3 (Duisterhof et al., 2022). In this sense, the AprilTag is “adjusted” by a detector that changes its own image representation and refinement scale according to the current camera model.

LFTag, although not an AprilTag family, is directly presented as actionable guidance for “adjustable AprilTags” when the design objective is to trade dictionary size against detection range by lowering spatial frequency (Wang, 2020). LFTag uses two larger baseline regions to resolve rotation and centroid-shift data regions that encode two bits each via four possible positions. Its capacity scales as

$$r_k^{(j)} \approx H_X\,\delta x_k + H_T\,\xi_j + \nu_k^{(j)},$$4

The comparative results are stark. LFTag 3×3 has a dictionary size of 16,384 versus 35 for AprilTag 25h9, and LFTag 4×4 has 268,435,456 versus 2,115 for AprilTag 41h12. In the synthetic range test, LFTag 3×3 reaches 27.8 m for both first missed and 20% missed detection, compared with 25.4 m and 27.1 m for AprilTag 25h9 at decimation 1 and 19.7 m and 19.7 m at decimation 2. LFTag 4×4 reaches 21.7 m and 21.7 m, compared with 17.5 m and 21.7 m for AprilTag 41h12 at decimation 1 and 14.1 m and 14.3 m at decimation 2 (Wang, 2020). On 266,995 tag-free LabelMe images, LFTag 3×3 produced 1 false positive and LFTag 4×4 produced 0, whereas AprilTag false positives depended strongly on family and ECC (Wang, 2020). The paper’s direct implication for adjustable AprilTags is to reduce spatial frequency, incorporate low-frequency anchors, add geometric and topological prefilters, and treat ECC as a parameter to be balanced against payload and false-positive behavior.

Several cross-cutting limitations recur across the literature. Stochastic modeling assumes zero-mean Gaussian perturbations in the tangent space of $$r_k^{(j)} \approx H_X\,\delta x_k + H_T\,\xi_j + \nu_k^{(j)},$$5, rigidly mounted static tags, known extrinsics, and at least one visible tag; very large gross tag errors or wrong tag IDs can still cause divergence (Kayhani et al., 2022). Recursive multi-scale markers improve robustness on curved surfaces and during proximity, but all systems fail when the quad becomes unrecoverable near edge-on views above about $$r_k^{(j)} \approx H_X\,\delta x_k + H_T\,\xi_j + \nu_k^{(j)},$$6–$$r_k^{(j)} \approx H_X\,\delta x_k + H_T\,\xi_j + \nu_k^{(j)},$$7 (Thakur et al., 25 Jun 2026). Dynamic identity-secure tags require trusted displays, trusted camera pipelines, and synchronization; desynchronization can increase FRR, and highly adaptive adversaries with fast electronic displays remain a concern unless keyed rolling codes are used (Li, 17 Aug 2025). AprilTags3D improves glare robustness, but extreme glare, motion blur, or large pitch/roll oscillations can still defeat all visible faces (Mateos, 2020). Family-level simplification can reduce RAM drastically, but the 24h10 case shows that this may worsen orientation ambiguity without improving detection rate (Springer et al., 2022).

A recurring misconception is that adjustability is synonymous with one specific tag redesign. The literature indicates something broader and more technically consequential: adjustable AprilTags are any AprilTag-based fiducial systems in which uncertainty, geometry, payload, codebook, viewing scale, detector representation, or physical arrangement is deliberately made conditional on task constraints. The resulting systems differ substantially in purpose—construction localization, autonomous landing, RPOD, wide-angle calibration, swarm latching, or identity-secured road infrastructure—but they converge on the same engineering principle: robustness is improved when the marker model is allowed to vary in a structured, explicitly parameterized way rather than being treated as fixed.