ABB quaternions calculation

Hello All

I need some answers for ABB quaternians . I am in develop of small appliation for ABB spray robots and there is necessary aply

the possibility for spray gun tilting (use angles ) .

Calculation in program is done . But calculated angles from quaternians do not give a sense .

For example ABB robot modul : where are quternians values like -> LOCAL CONST robtarget p_201_013:=[[550,366,100],[0.128860,0.695266,-0.695266,-0.128860],[0,0,0,0],[9E+09,9E+09,9E+09,9E+09,9E+09,240.925]];
This quaternians values should by after conversion to eulers 0 for all xyz . But is't. It is x 159, y 0 ,z -90 .

Could somebody explain if robot system calculate the 0 from base axis or from axis of world object or axis of tool .

Thanks .

Dear Hermann

Thanks for your reply .

I use calculations from wikipedia

From Q to E :

struct Quaternion
{
double w, x, y, z;
};

// This is not in game format, it is in mathematical format.
Quaternion ToQuaternion(double roll, double pitch, double yaw) // roll (x), pitch (y), yaw (z), angles are in radians
{
// Abbreviations for the various angular functions

double cr = cos(roll * 0.5);
double sr = sin(roll * 0.5);
double cp = cos(pitch * 0.5);
double sp = sin(pitch * 0.5);
double cy = cos(yaw * 0.5);
double sy = sin(yaw * 0.5);

Quaternion q;
q.w = cr * cp * cy + sr * sp * sy;
q.x = sr * cp * cy - cr * sp * sy;
q.y = cr * sp * cy + sr * cp * sy;
q.z = cr * cp * sy - sr * sp * cy;

return q;
}

From E to Q :

struct Quaternion {
    double w, x, y, z;
};

struct EulerAngles {
    double roll, pitch, yaw;
};

// this implementation assumes normalized quaternion
// converts to Euler angles in 3-2-1 sequence
EulerAngles ToEulerAngles(Quaternion q) {
    EulerAngles angles;

    // roll (x-axis rotation)
    double sinr_cosp = 2 * (q.w * q.x + q.y * q.z);
    double cosr_cosp = 1 - 2 * (q.x * q.x + q.y * q.y);
    angles.roll = std::atan2(sinr_cosp, cosr_cosp);

    // pitch (y-axis rotation)
    double sinp = std::sqrt(1 + 2 * (q.w * q.y - q.x * q.z));
    double cosp = std::sqrt(1 - 2 * (q.w * q.y - q.x * q.z));
    angles.pitch = 2 * std::atan2(sinp, cosp) - M_PI / 2;

    // yaw (z-axis rotation)
    double siny_cosp = 2 * (q.w * q.z + q.x * q.y);
    double cosy_cosp = 1 - 2 * (q.y * q.y + q.z * q.z);
    angles.yaw = std::atan2(siny_cosp, cosy_cosp);

    return angles;
}

The problem is that as you wrote abowe that same axis of tool and Wobj do not give the zero rotation . Wobj is rotated in 130° on X from world .

I am not ABB technician I must create application for robots witch was set by another company .

Thanks Juraj .

Quote from MOM

Using my tool I get the same result

Thanks for reply MOM ,

That means calculation is good .

Question is if there is set Wobj and the tool . And if I understand correctly or not , tool axis are set as in same position as Wobj axis after the rotation of tool should be 0 or not ?

Or it is calculated form world axis ?