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Controlling a robot autonomously involves two aspects.

Path planning and
Path tracking or path following.

Since you already have your path, you need to concentrate on path tracking. There are a few well established techniques for path-tracking such as potential field based ( there are many variants of this. Most obvious variant is Vector Field approach. These techniques assume that you know your map. There are other path tracking algorithms that work without a map too.

The package you mentioned in the answer uses Potential field based approach ( If I am not wrong). If you want to learn how path-tracking is done, pick an algorithm and try to implement it by yourself. You will learn better.