Autonomous Navigation Algorithm for Robot without know the map

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I'm still learning, but you need to use come kind of SLAM (simultaneous localisation and mapping) approach if you want to navigate through an unknown map. Basically, to navigate in an unknown space, you need to know where you are, and know what's around you. So, to work out what's around you, you need to look (in your case, using LIDAR), but you can't know what you're looking at if you don't know where you are. So you use your estimation of your position to estimate the map, and your estimation of the map to estimate your position. It sounds impossible, but over time, the approach can work, as long as you have tuned the system correctly.

I've heard of gmapping, hector, and amcl. I would check out the wiki for these pages.

Once you have SLAM implemented, I think that Jordan's answer will help you explore effectively.