Can computer sticks run ROS? (intel compute stick)

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You cannot really install things on the Intel Compute Stick like you're thinking, its not a computer, its just an additional [thing] to offload computations to, where you talk to it over their SDK, which handles all the Stick communication and transfers.

When we talk about using it with ROS, it's really more that there's a ROS wrapped version of their SDK you can use (in their case, its a service server you can query images for detection/classification that Intel suppors). In general though you just need to learn their SDK and use it in your ROS code.