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I want to move the controller forward and backwards at a certain speed, move it up and down, move it on a locus/non linear trajectory, etc. How would one go about doing this?

I'd use a model plugin and make direct physics calls to apply forces to the model.

I thought about using 'actors' but actors are unaffected by physics and so the sensors (imu sensor) does not work.

Yeah, actors are animations, so not appropriate here. I'd use a box with sensors, and make sure to give it reasonable inertia values.