I know of pairing functions, but my problem may involve three to five variables. When I have a few robots configured with certain parameters for movement, and I want to evaluate the robots based on how fast ($F$), how jerky ($J$) and how much energy ($E$) they consume, is there a statistical/mathematical technique of choosing the robot that has a high value of $F$, $J$ and $E$?
Eg:
$F$ range = $[0; 100]$, $J$ range = $[0; 1]$, $E$ range = $[0; 100]$
Assume $F$ and $E$ are normalized to range $[0; 1]$
Robot1: $F = 0.2, J = 0.9, E = 0.5$
Robot2: $F = 0.5, J = 0.6, E = 0.5$
Robot3: $F = 0.9, J = 0.9, E = 0.2$
Robot4: $F = 0.6, J = 0.2, E = 0.7$
I need a method of choosing Robot2, because although Robot3 has excellent values for $F$ and $J$, it's $E$ is low. But Robot2 has reasonable values for $F$, $E$ and $J$. I may eventually use more variables than just $F$, $E$ and $J$.
ps: Already saw this, this, this and this, but they don't answer the question.
The way your question is made it does not have a definitive answer. Because you haven't defined what is optimum in your setting.
But I think that you are asking for ideas to define the optimum. So, I'll throw some ideas:
You may interested in minmax, a weighted average, the geometric mean or a generalized mean or other types of average.
From what you said, it seems to me that either the geometric mean or a weighted average could work out.
Another idea was to use something like:
Choose the robot with the highest $F + J + E + k \min(F, J, E)$. Choose the value of $k$ according to your feeling, but you may start by trying $k=1$.