Coordinate Frame Transformations in ENU Don't Match The Standard

[P3TE]

Describe the bug

In Unity, to convert a vector from unity space RUF (Right, Up, Front) to ENU (East, North, Up), the following transformation is applied:
public Vector3 ConvertFromRUF(Vector3 v) => new Vector3(v.x, v.z, v.y);
This assumes that in Unity a positive x is East, a positive z is North and a positive y is up.
However, to convert a rotation from Unity space RUF (Right, Up, Forward) to ENU (East, North, Up), the following transformation is applied:
public Quaternion ConvertFromRUF(Quaternion q) => new Quaternion(q.x, q.z, q.y, -q.w);
This however assumes when in Unity, an identity rotation (When the forward vector is positive z (0, 0, 1)) would also be an identity rotation in ENU.
This means that in Unity, when facing z forward or North, the orientation in ENU is also the identity.
However in ENU, when the rotation is identity, forward should be facing East, see:
"In case of land vehicles like cars, tanks etc., which use the ENU-system (East-North-Up) as external reference (World frame), the vehicle's (body's) positive y- or pitch axis always points to its left"

Image from Wikipedia shows the zero point on the yaw to be East, rotating counter-clockwise

• https://en.wikipedia.org/wiki/Axes_conventions#World_reference_frames_for_attitude_description

The problem seems to be that:
Unity geographic coordinates have +x = East, +y = Up and +z = North, but when converting geographic rotations offsets are not taken into account 0 = North when it should be 0 = East (In ENU terms).

We found this discrepancy to be an issue when using Unity to simulate IMU data (converted to ENU before publishing) which would then be fed into the ROS robot_localization package. When doing this, we found that we would be pitching when the object was rolling in Unity and vise versa. The robot_localization link provided indicates that ENU should be used for all IMU data. Switching the conversion to FLU and re-framing our environment such that -x = North, +y = Up and +z = East corrected this discrepancy.

To correctly convert a rotation from Unity space to ENU, either:

1. Unity should be -x = North, +y = Up and +z = East and ENU transformations should be equivalent to FLU transformations. (Note: This would probably break NED rotational transformations)
   OR
2. Unity should apply a yaw offset of 90 degrees when converting from Unity orientations to ENU orientations and vice versa.

Is there something else about the Unity implementation that I am missing?

Some related links

• REP-103 Standard Units of Measure and Coordinate Conventions
• REP-105 Coordinate Frames for Mobile Platforms
• REP-145 Conventions for IMU Sensor Drivers

[P3TE]

After some testing, we have found the implementation for option 2 should look something like this:

    public class ENU_GeoSpacial : ICoordinateSpace
    {
        public Vector3 ConvertFromRUF(Vector3 v) => new Vector3(v.x, v.z, v.y);
        public Vector3 ConvertToRUF(Vector3 v) => new Vector3(v.x, v.z, v.y);

        private static Quaternion rotationalOffset = Quaternion.Euler(0, -90,  0);
        private static Quaternion inverseRotationalOffset = Quaternion.Euler(0, 90,  0);

        public Quaternion ConvertFromRUF(Quaternion q)
        {
            q = q * rotationalOffset;
            return new Quaternion(q.x, q.z, q.y, -q.w);
        }
        public Quaternion ConvertToRUF(Quaternion q)
        {
            q = new Quaternion(q.x, q.z, q.y, -q.w);
            return q * inverseRotationalOffset;
        }
    }

[hyounesy]

Thanks for reporting the issue. We will investigate and return back to you.
[Ticket# AIRO-1188]

[peifeng-unity]

Thanks, @P3TE for reporting the issue. We have made a PR to fix it.

[P3TE]

Thanks.
Ah, so within Unity, the coordinate system we should be using is: x=South, y=Up and z=East.

[P3TE]

Hi, looking through the PR, I noticed that while this fixes ENU, NED will now be out be 90 degrees.
The problem is similar to the original, but essentially, a yaw of 0 (The identity quaternion) in NED corresponds to north.
However, in the PR, a Unity identity quaternion (z-forward direction) when converted to NED would also produce an identity quaternion which would be incorrect as z is recognised as the East direction.
See:

Image from Wikipedia shows the zero point on the yaw to be North rotating clockwise

• https://en.wikipedia.org/wiki/Axes_conventions#World_reference_frames_for_attitude_description

[peifeng-unity]

Hi @P3TE, thank you for taking a look at the PR. I might misunderstand you, but it seems to me that the NED conversion in the PR (as shown below) put the z-axis in the "Down" direction (-v.y), which seems the same as the image you've shown. Please correct me if I made mistakes.

public Vector3 ConvertFromRUF(Vector3 v) => new Vector3(-v.x, v.z, -v.y);

[P3TE]

Hey @peifeng-unity,
The issue is only with rotations, the Vectors are fine.

The issue is that:

• In ENU, A Yaw of 0 degrees represents East, 90 Represents North, 180 West and 270 South. So from a top down view, it's a counter clockwise system, typical of how you would think of rotations in 2D.
• In NED, A Yaw of 0 degrees represents North, 90 Represents East, 180 South and 270 West. So from a top down view, it's a clockwise system.

To convert a yaw from ENU to NED you would have:
YawNED = 90 - YawENU and the same for converting NED to ENU YawENU = 90 - YawNED

However for a simple case Quaterion, the identity (x, y, z, w) = (0, 0, 0, 1):
In Unity that would produce an orientation with the forward vector of (0, 0, 1). (East)
When converted to:
ENU: public Quaternion ConvertFromRUF(Quaternion q) => new Quaternion(q.z, -q.x, q.y, -q.w);, so the Quaternion becomes (0, 0, 0, -1)
Which is still the identity rotation, so the forward vector (ENU) would be (E, N, U) = (1, 0, 0). (East) which is fine.
However for NED:
NED: public Quaternion ConvertFromRUF(Quaternion q) => new Quaternion(-q.x, q.z, -q.y, -q.w);, so the Quaternion becomes (0, 0, 0, -1).
Which is also the identity rotation, so the forward vector would also be (N, E, D) = (1, 0, 0). (North) which for NED doesn't make sense since the rotation in Unity faces towards the East. It should be something along the lines of (0, 0, (√2)/2, (√2)/2).

Let me know if this is making sense, I could try make some diagrams of the issue if that would help.

[peifeng-unity]

Ah, thank you! I think I got it. After the vector conversions from RUF to NED, the rotation needs to rotate for 90 more degrees (clockwise) with the z-axis (yaw) so that the body could facing to the east for the identity rotation. This makes sense to me. I will create a new PR for it.

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