"I would like to know if there is a function that changes the input angles to minimise all six elements in the output error vector?"
Add weighting to the error values if required (e.g. square the values), then sum them. Minimize the sum. Any "minimizing of the vector" will ultimately be exactly equivalent to this, so that is the solution. You could use lsqnonlin (which requires a vector output from the cost function), but note that this implicitly sums the squares of the vector, so it amounts to exactly the same thing.
