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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.
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.
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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.