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If you're navigating without a map, then your robot will only be using distances and bearings to get to places. Therefore the robot will need to measure distance and bearings. To get to different waypoints it would be simply geometry to get to one point or another with the accuracy depending on how well your robot tracked its path (dead reckoning).

If there is not SLAM or map then the idea of a planner is redundant. The robot just needs a start point and a list of navigation points that can be determined in relation to the start point.