apply the inverse kinematic tranformation?

[Ether]

Originally Posted by Mike Betts

forward kinematics ... yields a unique result.

In the case of the velocity kinematics of the mecanum vehicle, it is the inverse kinematic transformation (from desired vehicle motion to required wheel speeds to achieve that motion) which has a unique result.

The forward kinematic transformation for a mecanum vehicle (from four arbitrary wheel speeds to the vehicle motion which would result from those wheel speeds) in general has no exact solution, but you can calculate a "least squares fit" to find the "best" approximate solution. This is discussed in this paper.