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I am learning the artificial potential field method for path planning of mobile robot; artificial potential field method has two components: the first one is attractive force and second one is repulsive force.

The repulsive function is defined as :

WhereUrepis repulsive field,P0is the distance of influence of the obstacle.Pis the distance between the mobile robot and obstacle.ƞis the proportional coefficient.(X-Xg)is the distance between the mobile robot and goal. The repulsive force is the negative gradient of this repulsive potential fields function.

My question is aboutFrep, what is the difference betweenFrep1 , Frep2and||Frep1||,||Frep2||.

WhyFrep1 & Frep2contain parts that rounded with red circles while||Frep1||,||Frep2||don’t contain?

What is the difference between two states? Could anyone explain that for me?

Thanks in advance

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