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For example when I clicked on some button, object will smooth move +20 pixel up. I made something like this with LiteTween but it moves X+20 about global X, so it goes off the screen. Making it relative value does't help.
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litetween should be able to do what you want... so try looking into the settings or make a small sample for us to look at...
the other way to do it would be to use lerp. which would work fine, but is a manual way to do what litetween does for you.
I am always using lerp for that purpose.
On start of layout update your object with a variable containing the original X and Y of the object.
Then move it relative to that.