However, I don't believe in full predetrminism, and you don't either. If you did, you would not think about improving the world, or convincing people of things - if you believe that the next speech by the president was determined at the time of the big bang, then thinking about change is meaningless, and none of us can help feel or not feel however we do.
However, if you believe in a world where the future has not happened yet and it evolves more like a complex computation, with room for changing program code by the program itself, perhaps even with some randomness thrown in, you get a fully naturalistic deterministic world where nevertheless you can try to influence things in some direction or another.
To articulate my own belief about this more clearly, I think the example of robots you gave is very good. I believe that even a robot with a simplistic machine learning algorithm can be meaningfully said to have a kind of free will, in that it can do a better or worse job at what it was designed to do based on the examples it is given and on accidents of its training process. Two such robots may well have different beliefs about the world (in a very basic sense)and they could even influence one another based on their experience (training set) and conclusions (parameters of their algorithm). This is how I believe humans and animals work as well - we have a pre-determined algorithm (vastly more complex), with different starting parameters between different people, we have a training set consisting of all of our lived experiences, and our algorithm can modify itself or its parameters during training, in pre-specified ways. This does end up meaning that some people end up with better models/algorithms than others, based on better starting conditions, or on more luck with experiences. And decision points in this algorithm are what I think represents our experience of free will.