Скачать или смотреть Converting ArUco Axis-Angle to Unity3D Quaternion

Discover how to accurately convert ArUco axis-angle rotations to Unity3D quaternions. Learn from the common pitfalls and the essential corrections needed for proper orientation comparison between the real world and simulations.
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Understanding the Problem: ArUco and Unity3D Quaternion Comparison

When developing augmented reality applications or gaming simulations, it's crucial that the orientation of virtual objects matches that of their real-world counterparts. A common scenario arises when using ArUco markers, where developers find themselves needing to compare the real-world orientation of an object, tracked by a marker, to its simulated version in Unity3D.

In this guide, we’ll explore how to convert ArUco's axis-angle representation into Unity3D's quaternion format. While approaching this problem, many encounter issues with the discrepancies between the orientations derived from both systems.

The Quaternion Format in Unity3D

Quaternions are used in 3D space to represent rotations. They are composed of four components: (x, y, z, w), where:

x, y, z represent the vector part of the quaternion

w represents the scalar part

In Unity3D, you can retrieve the quaternion of an object with the following code:

[[See Video to Reveal this Text or Code Snippet]]

The ArUco Marker Conversion

ArUco markers provide a compact representation of rotations, which can be obtained through the estimatePoseSingleMarkers function in OpenCV. The result is often in the form of an axis-angle representation, which needs to be converted into a quaternion.

The Conversion Function

The conversion requires a custom Python function, which can be seen below:

[[See Video to Reveal this Text or Code Snippet]]

In this function:

rvecs is the rotation vector output from the estimatePoseSingleMarkers.

We calculate the angle theta and create a unit vector b before deriving the quaternion components.

Addressing Common Issues

Despite using the conversion function correctly, discrepancies in results may still arise. For example, you may see output like:

ArUco Result: [0.9464098048208864, -0.02661258975275046, -0.009733748408866453, 0.321722715311581]

Unity's Result: [-0.492555320262909, -0.00628990028053522, 0.00224017538130283, 0.870255589485168]

The Root Cause

One common issue that developers face is the location of the ArUco marker on the object being tracked. If the marker is positioned in such a way that it is inherently rotated (e.g., mounted on top of the cube rotated by -90 degrees), this will render the quaternion calculations inaccurate.

The Solution

To correct this, follow these steps:

Adjust the Pivot Point: Change your pivot in Unity to rotate it by -90 degrees. This adjustment effectively corrects the orientation.

Apply Quaternion Adjustment: After obtaining the quaternion from ArUco, apply the transformation:

Convert the quaternion as follows:

[[See Video to Reveal this Text or Code Snippet]]

This modification should align the orientations of the real object and the simulated object accurately.

Conclusion

Converting axis-angle to quaternion for ArUco markers in Unity3D can initially seem daunting, especially when unexpected discrepancies arise. However, by adjusting your pivot and accounting for the orientation correctly, you can accurately compare the real-world and virtual object orientations. This will ensure a coherent augmented reality experience or simulation.

If you're still encountering issues, consider revisiting the positions of your markers and ensure that the calculated quaternions are being transformed correctly.