Control allocation roll/pitch torque effectiveness actual meaning

Thank you Henry for this extremely well written explanation! Going further from your comments, I still wonder the following:

  1. The normalized matrix determines the ā€œrelativeā€ scale of deflection each actuator will have, but how does the ā€˜absolute valueā€™ get determined (-1 ā€¦ +1 range for elevons for example)?

  2. Regarding what the ā€˜normalization factorā€™, I believe the absolute maximum torque that can be generated with combination of ALL actuators will have to equal 1.0 (after being normalized), instead of ā€˜Biggest torque generatable from any of actuatorā€™. Is this not true?

The second question was raised, as after thinking about why the Flying Wingā€™s elevons each have +/- 0.5 effectiveness for roll torque (instead of +/- 1.0, or 2.0, etc.), I have concluded that the maximum roll torque that can be generated with those actuators then equal 1.0 (= +1 x +0.5 + (-1) x (-0.5)), which relates back to the first question on how absolute value gets derived.

Would love to hear your thoughts on these two points!

Note: Seems like this issue is related to the normalization situation in PX4ā€™s control allcoation: