**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.

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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By Zacobria Lars Skovsgaard

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