Supported Turtlebot Sensors? - inc. Raspberry Pi

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Quick advice: Don't get the "Astra Pro", get the regular "Astra" instead (see my answer here).

To me, the Orbbec Astra is the best replacement for the ASUS Xtion Pro that you can get at the moment. Quality-wise, it's almost as good as the Xtion, and it's OpenNI2-compliant, so it's a drop-in replacement for the Xtion in most cases.

There are still a few kinks with the ROS drivers, so you need to fiddle around a bit before you figure out which combination of driver version and parameters gives you full framerate registered point clouds and no artifacts at object edges, but it's possible.

I've successfully run the Astra on an ARM SBC (the Odroid XU4), so I don't see why it shouldn't work on a RPI3. There are even binary ARM packages available for ROS.