Why do we choose square rather than other formula (like absolute) as our objective function? Will they produce a totally different output or the result changes just a bit?
So in the case of our A4, we should apply the f_0 equation here to the Newton's method of higher order descent here http://15462.courses.cs.cmu.edu/fall2018/lecture/optimization/slide_027?
How does this deal with the problem of having multiple configurations that get to the target? Will it always give the same solution?
@yongchi1 No fundamental reason to use the square, other than that it has easy derivatives. You could use something else, but it may become harder to evaluate/solve.
@tcl1 Nope, the solution to an IK problem is not generally unique. If you want "nicer" solutions you can think about how to "regularize" the problem. For instance, you can look for angles that not only meet the goal, but are also close to the initial angles. Or are as small as possible. Or are as similar as possible to each-other. Etc.