left_hand_to_quaternion

左手系转四元数 §

• Unity的空间采用的是左手系，如果将其中的数据传递给ROS（如使用VR设备时对手/头的位置进行追踪），其中一种方式是将Unity的世界坐标转化为ROS的四元数，这样可以直接用ROS的geometry_msg中的数据类型进行表示。例如PoseStamped或者TransformStamped都是用四元数表示角度（例如PoseStamped().pose.orientation或者TransformStamped().transform.rotation）。

• 分为两步，第一步：直接通过Unity的API获得代表旋转的四元数；第二步：将左手系的四元数转化为右手系

• 转换关系：

  		Unity	ROS/righthand
  translation	x	xunity	-zunity
  	y	yunity	xunity
  	z	zunity	yunity
  rotation	x	xunity	-zunity
  	y	yunity	xunity
  	z	zunity	-yunity
  	w	wunity	wunity

• 代码

  Vector3 pos = targetCamera.position;
  Quaternion rot = targetCamera.rotation;
   
  string output = (-pos.z).ToString("0.00") + ',';
  output += pos.x.ToString("0.00") + ',';
  output += pos.y.ToString("0.00") + ',';
   
  output += (-rot.z).ToString("0.0000") + ',';
  output += (rot.x).ToString("0.0000") + ',';
  output += (-rot.y).ToString("0.0000") + ',';
  output += (rot.w).ToString("0.0000") + ',';
  return output;

参考StackExchange

A quaternion can be thought of as an angle-axis representation:

quaternion.xyz = sin(angle/2) * axis.xyz
quaternion.w = cos(angle/2)

So, converting them between two coordinate systems can be broken down into two steps:

Map the axis into the new coordinate system.

If changing between left & right hand coordinates (eg. if there’s an odd number of axis negations or axis exchanges between the two), negate the angle.

Since cos(-angle) = cos(angle) and sin(-angle) = -sin(angle) this is the same as flipping the axis of rotation, negating the x, y, and z parts.

Taking your specific example:

	sensor	unity
forward	x	z
up	z	y
right	-y	x

We can combine these steps into:

Quaternion ConvertToUnity(Quaternion input) {
    return new Quaternion(
         input.y,   // -(  right = -left  )
        -input.z,   // -(     up =  up     )
        -input.x,   // -(forward =  forward)
         input.w
    );
}