You're talking about Universal Basic Income, which is one possible solution to the very real problem manual labor will face in the near future. With manual labor being increasingly automated, the question at hand is "what will people do?"
However, in your world everything is automated, and there is no currency to act as a value placeholder, so your basic income will be some amount of resources. Now, not everyone has need of the same amount or type of resources, so if your AI is adhering to the tenets of communism* (see Matt's answer) "...for each, according to need", everyone will get different amounts and types of resources based on personal need.
Some resources, being more finite, will be worth more in a "market" sense, but not necessarily worth more within your need-based society. So from an outside perspective, you will have "rich" and "poor", as some people will have a greater share of valuable resources, however, within your society those people will likely not be viewed as such. If everyone has what they need, and not more, to contribute fully to society, everyone is effectively equal. The fact that some have overall greater "value" than others is irrelevant.
*Pure ideological communism is often described as "from each according to ability, for each according to need". This is a pretty functional description of the ideology behind communism, though lacking in implementation.