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C# code Example of converting RPY/Euler angles to Rotation Vector/Angle Axis for Universal-Robots.

C# code Example of converting RPY/Euler angles to Rotation Vector/Angle Axis for Universal-Robots.
Orginal Post by Mathias Siig Nørregaard.

Here’s my C# implementation based on Erwin’s math. I noticed you have to change the theta value depending on the sign of your roll. At least this works for me… please point out any flaws. Thanks.
Given a direction vector, convert that to a roll and a yaw and convert that to a rotation vector:
Link to code.

 

/// <summary>
/// Gets the roll pitch and yaw from a direction vector. 0,0,0 is up.
/// </summary>
/// <param name="d">Direction vector. Must have a length of 1</param>
public Vector3 ToRollPitchYaw(Vector3 d)
{
 d = Extensions.Normalize(d);
 double roll, pitch = 0, yaw = 0;
 double pi = Math.PI;
 roll = Math.Acos(d.Z);
 if (d.X == 0 && d.Y == 0)
 {
 yaw = 0;
 }
 else
 {
 Vector3 noZ = new Vector3 { X = d.X, Y = d.Y, Z = 0 };
 noZ = Extensions.Normalize(noZ);
 if (d.X <= 0)
 yaw = -Math.Acos(-noZ.Y);
 else
 yaw = Math.Acos(-noZ.Y);
 }
 if (pitch < -pi)
 pitch = 2 * pi + pitch;
 else if (pitch > pi)
 pitch = pitch - 2 * pi;

 Vector3 rpy = new Vector3 { X = (float)roll, Y = (float)pitch, Z = (float)yaw };
 return rpy;
}

/// <summary>
/// Converts a roll pitch yaw vector to a rotation vector.
/// </summary>
/// <param name="d">A vector where X=Roll, Y=Pitch, Z=Yaw</param>
/// <returns>A rotation vector with rx, ry and rz used to rotate the TCP of UR10</returns>
public Vector3 ToRotVector(Vector3 rpy)
{
 float roll = rpy.X;
 float pitch = rpy.Y;
 float yaw = rpy.Z;
 if (roll == 0 && pitch == 0 && yaw == 0)
 return new Vector3 {X=0, Y=0, Z=0};
 Matrix3 RollM = new Matrix3();
 RollM.M00 = 1; RollM.M01 = 0; RollM.M02 = 0;
 RollM.M10 = 0; RollM.M11 = Math.Cos(roll); RollM.M12 = -Math.Sin(roll);
 RollM.M20 = 0; RollM.M21 = Math.Sin(roll); RollM.M22 = Math.Cos(roll);

 Matrix3 PitchM = new Matrix3();
 PitchM.M00 = Math.Cos(pitch); PitchM.M01 = 0; PitchM.M02 = Math.Sin(pitch);
 PitchM.M10 = 0; PitchM.M11 = 1; PitchM.M12 = 0;
 PitchM.M20 = -Math.Sin(pitch); PitchM.M21 = 0; PitchM.M22 = Math.Cos(pitch);

 Matrix3 YawM = new Matrix3();
 YawM.M00 = Math.Cos(yaw); YawM.M01 = -Math.Sin(yaw); YawM.M02 = 0;
 YawM.M10 = Math.Sin(yaw); YawM.M11 = Math.Cos(yaw); YawM.M12 = 0;
 YawM.M20 = 0; YawM.M21 = 0; YawM.M22 = 1;

 Matrix3 Rot = new Matrix3();

 //rot = yaw * pitch * roll
 Rot = Matrix3.Dot(YawM, Matrix3.Dot(PitchM, RollM));

 double rotSum = Rot.M00 + Rot.M11 + Rot.M22 - 1;
 double alpha = Math.Acos(rotSum / 2);
 double theta = 0;
 if (roll >= 0)
 theta = alpha;
 else
 theta = 2 * Math.PI - alpha;
 double my = 1d / (2 * Math.Sin(theta));

 double rx = my * (Rot.M21 - Rot.M12) * theta;
 double ry = my * (Rot.M02 - Rot.M20) * theta;
 double rz = my * (Rot.M10 - Rot.M01) * theta;

 Vector3 rotationVector = new Vector3();
 rotationVector.X = (float)rx;
 rotationVector.Y = (float)ry;
 rotationVector.Z = (float)rz;
 return rotationVector;
}

 

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