How do I make an Android app to access the GPIO of the BeagleBone Black?
Most of the work needs to be done on the beaglebone side. You need to write an API - and I would recommend RESTful (google it) - to expose any GPIO functionality you need. Then you can use this API from your Android device, which is the easy part.
You should find instructions on how to write such an API. Another term that is closely related to this API is IoT (Internet of Things). An example of such an API (IoT framework (for Raspberry pi webiopi . You can see this guide on how to build a restful api on pi.
I'm afraid there isn't much documentation available for Beaglebone, but hopefully you've got a picture of what you should be looking for or implementing.
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