What Are the Differences Between Frep1, Frep2, and Their Magnitudes?

[Maria88]

Hello all

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 :

Where Urep is repulsive field, P0 is the distance of influence of the obstacle. P is the distance between the mobile robot and obstacle. ƞ is 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 about Frep , what is the difference between Frep1 , Frep2 and ||Frep1|| , ||Frep2||.
Why Frep1 & Frep2 contain 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

 

[certainly]

Well, If you're talking about the circled parts those are partial derivatives.

 

[Maria88]

Well, If you're talking about the circled parts those are partial derivatives.

Thanks a lot "certainly", I am really appreciated that for you, thanks for nice explanation, actually the general idea of potential field method is clear to me, the problem which I face is in the repulsive potential field function and specially after taking the negative gradient I became a little bit confused where in some book I find that repulsive function in shape of ||Frep1|| , ||Frep2|| is considered and other book the repulsive function in shape of Frep1 , Frep2 is considered I need help to understand which one I should considered and why parts that rounded with red circles (which mean partial derivative if I am not wrong) are removed from modules ||Frep1|| & ||Frep2|| and from Frep1 , Frep2 are not .

Mybe my questions are so silly please forgive I am still beginner.

Thanks

 

[certainly]

I don't know too much about these equations but in general, ||A|| is equal to the magnitude of A.
Well if $X_g$ is constant the second circle should be 1. Also what is $X$ ? If $X$ is the distance traveled by the robot from the starting point and assuming that the obstacle is directly between the robot and the goal (I imagine it wouldn't be called an obstacle otherwise!) then you can see that $\rho=C-X$ where $C$ is the distance between the starting point and the obstacle. Therefore the first circle must be -1.