Is it possible to allow an Android/iOS app accessing my SmartThings hub and does some simple control, like turning on a light switch? I want the app to be able to see the devices paired up with my SmartThings hub, e.g., all light switches, and be able to turn them on/off. Do the SmartThings APIs allow me to do this?
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Yes, you can do this with the SmartThings API.
If you prefer something off the shelf that you can customize as you see fit, be sure to check out SharpTools.io
The Home Remote is another option.
It works well. It is a bit of learning curve setting it up. Extremely powerful.