Not sure if the question is about the simulator Caladan, or about our autonomy core.
For Caladan, we don't support playback of data currently. Do you have a use-case need for this?
For the autonomy core, the localization, costmap generation, and path planner are all probabilistic to a more or less degree, so we can't guarantee determinism to any highly accurate degree. However, if the same data is played back over and over, the vehicle would react in basically the same way (perhaps not navigating to the exact same spot, but within a small tolerance). Same question here; what is your need/use case to have guaranteed determinism? Is it a safety question? (We can have a much longer chat there)