IK on legs works only after you rotate a bone in the IK chain I've been having this problem for a while. So I have a rig for a robot I am doing and the arm IKs are working as expected.
But when I move the leg IKs the IK isn't working. 

The first half of the image is the original position of the IK target.
But when I rotate slightly a bone in the IK chain it works properly.


Here is the blend file with the rig:
https://www.dropbox.com/s/6zrcv0caqeh8pmd/rigg.blend?dl=0

I've been trying to figure out the problem for a while but I can't solve it. I don't even know how to google it, couldn't find anything.

A pole target might solve it but I can't use it since as far as I can see I won't be able to limit the rotation of the IK bones.
First of all, if you don't want to add a pole bone (and I didn't understand why) in edit mode you can slightly move forward (Y axis) the knee bone: in this way the IK solver will try the front movement as first solution.

In a IK chain, limits should be set in the properties panel, bones, Inverse Kinematics tab, instead of bones constraints (this has to be done for every bone of the chain).

In your file all thoose values are wrong: I don't know which kind of constraint you need but I suggest you to remove all constraint and readd them one by one (the red line shows the allowed movement of every bone).