move_base without global planner

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The global planner is a key part of move_base; it finds the global path between the start and end state. Why do you want to disable it?

Maybe I misunderstood the concept of global planner and confused it with global map. So even if I don't have a global map and my target is near the robot I still need the global planner? Do global planner great a path to target and local planner how to achieve next point on the target?

Yes. The global planner creates the path, and the local planner executes the path. I've seen a few posts on this forum about running the global planner without a global map, but I haven't tried it myself.