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Start thinking that the spatial derivative (or gradient) of the potential field represents a force. By applying this force at the robot end-effector you can use operational (or cartesian) space control (see O.Khatib) or translating this force in joint torques by means of Jacobian transpose.

This paper is one of the milestones in the artificial potential field:

http://cs.stanford.edu/group/manips/publications/pdfs/Khatib_1986_IJRR.pdf

Basicly, it explains how to model both attractive potential field (for the desired pose) and repulsive potential field (for the obstacles). This two potential field have always different signs. You can make use of quadratic function, e.g.

U = ½ (x - xc)^2

which is positive, continuous and differentiable function which attains zero when x=xc and where xc is the vector position center of the modelled obstacle or of the goal position. Once all objects have been modelled using this kind of functions you have simple to differentiate all the U obtaining respective forces F. This forces should be added together for calculating the overall force at the robot tip.

If you have a simulator accepting joint torques as input, lets say V-REP, all that you have to do is multiply the resulting force for the Jacobian transpose matrix that is function of the joint positions.

Obviously, there are several ways to model obstacles, using different functions, and several ways to keep the stability of the simulation. For further details have a look into the literature or don't hesitate to ask again!

Good luck ;)