How to convert two 3D coordinates to Euler angles?

I have two vectors representing (lat, long, alt). I need to calculate the Euler angles (roll, pitch, yaw) required to go from vec1 to vec2. I tried making a rotations matrix and then use rotm2eul() function but I keep getting an error, seen below? The rotation matrix is not of the same format that rot2eul() expects but I am unsure how to fix it. Also, my altitude is in meters, and lat long is in degree so would I need to convert to a common unit?

Error message: Error using rotm2eul Expected R to be of size 3x3xM, but it is of size 1x4.

Error in robotics.internal.validation.validateRotationMatrix (line 21) validateattributes(R, {'single','double'}, {'nonempty', ...

Error in rotm2eul (line 33) robotics.internal.validation.validateRotationMatrix(R, 'rotm2eul', 'R');

Error in S1_NoAcc_3_glide3 (line 346) eul = rotm2eul(rotm);

x_earth = 76.9470;
y_earth = 38.9948;
xnew = 76.9492;
ynew = 38.9935;
hi = 150; % m 
hf = 0; 
vec1 = [x_earth, y_earth, hi];
vec2 = [xnew, ynew, hf];
rotm = vrrotvec(vec1, vec2); % generate rotation matrix
eul = rotm2eul(rotm);

[Jan]

Please post the complete error message, such that we do not have to guess, which error occurs where. Thanks.

There is no "common unit" for meters and degrees. You need a reference system to determine the rotation matrix and in your case there is a translation also.

[Andrew Poissant]

Thank you, I have updated the question to include the error message.

Answer 1

[Jim Riggs]

According to the documentation for function vrrotvec, the output of this function is a rotation vector, not a rotation matrix. vrrotvec provides a 4-element row vector output; the first three elements are the rotation vector axis, and the fourth element is the rotation angle.

Function rotm2eul is expecting a 3x3 rotation matrix (i.e. a direction cosine matrix) as the input argument.

[Andrew Poissant]

How would I go about finding the direction cosine matrix with my two vectors?

[Jan]

@Andrew: Two vectors do not define a direction cosine matrix uniquely. So you need more information.

[Andrew Poissant]

So I can't calculate pitch angle of an aircraft given initial position and altitude and final position and altitude?

[Jim Riggs]

There is a way to compute a direction cosine matrix from a rotation vector. Given:

hrot = vrrotvec(vec1,vec2);  % rotation vector elements

we can calculate the DCM from hrot. To begin, we calculate the rotation vector from hrot:

angle = hrot(4);
Vrot = angle*[hrot(1) hrot(2) hrot(3)];  % This is the rotation vector

Next, define the function vcross as:

vcross = @(v) [0 -v(3) v(2); v(3) 0 -v(1); -v(2) v(1) 0];

Now the direction cosine matrix can be computed using:

DCM = eye(3)+ (sin(angle)/angle)*vcross(Vrot) + ((1-cos(angle))/angle^2)*vcross(Vrot)*vcross(Vrot);

[Jim Riggs]

After looking back over this thread, it appears that I am answering the wrong question here. The question I was addressing was " I need to calculate the Euler angles (roll, pitch, yaw) required to go from vec1 to vec2."

I interpreted this as rotating vector 1 to align with vector 2. This is in fact what the function vrrotvec does, but it gives the components of a rotation vector (axis and angle). This can be converted into a direction cosine matrix, and this is the method that I have provided, above.

After looking at the conversation thread, it would appear that this is not the problem you wanted to solve. In fact, if you are trying to get the euler angles of the aircraft located by position vectors vec1 and vec2, there is absolutely no way to do this, because position vectors contain absolutely no information regarding the attitude of the body. (In rigid body dynamics, Chasle's theorem takes advantage of this and allows for the separation of the linear and angular degrees of freedom into separate problems) So, the position of the body will not help you find it's attitude. @Jan is quite right - you need more information.

[Andrew Poissant]

Excuse my ignorance, but this is not as straightforward as using trigonometry to find the pitch angle required of the aircraft to reach vec2?

[Andrew Poissant]

Isn't pitch proportional to altitude?

[Jim Riggs]

@Andrew: In this case, you are assuming that the aircraft is at position 1 given by vec1 and some time later it is at position 2, located by vec2. The course of the aircraft is along the vector (vec2-vec1), but this does not really specify the attitude of the aircraft. If you assume that the aircraft traveled in a straight line from (1) to (2), zero angle of attack, and zero sideslip then the aircraft attitude will align with the course line (but only if there also is no wind). You will also need to assume a bank angle in order to completely define the set of Euler angles. So you see, it takes a lot of assumptions to get from a course line to the attitude.