Task weighting is performed by multiplying task matrix A and task vector y by a weight value w.
in this way, it's like stretching the space to have larger or smaller contribution with the square norm
In current implementation, (see velocity scene for example), y vector is not multiplied by the task weight. the resulting problem is
minimize x'(wA)'(Wa)x - (wAx)'y
dmronga
commented
3 months ago
Task weighting is performed by multiplying task matrix A and task vector y by a weight value w. in this way, it's like stretching the space to have larger or smaller contribution with the square norm
|| w(Ax -y) || -> || (wAx - wy) || -> minimize x'(wA)'(Wa)x - (wAx)'wy
In current implementation, (see velocity scene for example), y vector is not multiplied by the task weight. the resulting problem is minimize x'(wA)'(Wa)x - (wAx)'y
https://github.com/ARC-OPT/wbc/blob/19c562dd3699f7581161bf6958dab29655624220/src/scenes/VelocitySceneQuadraticCost.cpp#L110-L115