Need clarification on potential fields for robotics

I am taking a course on AI robotics from a computer science department but my background is in mechanical engineering. I am having some difficulty with ambiguous terminology in virtual potential fields. All of the sources I have seen to define the virtual potential fields with a physics basis: $$F(q) = \nabla U(q)$$ or that the force imposed by the potential field is the gradient of the potential function.

Then, the CS sources I have seen will later set the velocity set point of the robot controller equal to:

$$\mathbf{q}_s = \nabla U(q)$$

essentially using the imposed force as a velocity setpoint. But none of the sources mention this swap. So am I missing something, or is the term virtual potential field sort of a misnomer? Maybe it should be virtual velocity potential field?

Here are some CS course slides I am looking at: http://cs.gmu.edu/~kosecka/cs685/cs685-potential-fields.pdf http://www.cs.cmu.edu/~motionplanning/lecture/Chap4-Potential-Field_howie.pdf

Thank you!

It is possibly a misnomer. We CS people shouldn't really be talking physics ;)

Nevertheless, the idea used here is quite simple. Simple enough that many people have "invented" it on their own before learning its existence. I believe the reason it's called a potential field is due to the way many people implement the idea.

Let's take an example. For me, the moment of "inventing" this method was in a head-to-head Snake game, so say you are navigating an environment where there is a goal you want to go towards but also dangerous locations you want to avoid. In the case of Snake, the goal was the apples and the dangerous locations were your and your opponent's bodies.

Now say you want to simply have a "tendency" towards the goal which is stronger the closer you are to it, and a tendency to avoid danger which is also stronger the closer you are to it. Out of purely non-scientific intuition, let's say the strength of this tendency ($T$) is relative to the inverse distance ($R$) squared. So:

$$T \sim \dfrac{1}{R^2}$$

(Naturally, there is a $\sum$ for every source of tendency)

In physics, "the strength is relative to the inverse of distance squared" looks like potential fields, and I believe that's where the name of this method came from.

Now in different applications of this method, you might do a different thing with the calculated $T$. You could use it in a physically meaningful way (as if it really were a potential field), but that often leads to problems. In the navigation problem above, you would likely end up orbiting your goal instead of reaching it. More easily, you could set your velocity to the same value as the strength of your potential field and screw physics.

• Thank you for the example, I understand the application pretty well, just a matter of semantics, I guess. And I do like your "strength relative to inverse distance squared" abstraction. Also FYI, after some digging in the literature, it does appear that the earliest examples (Khatib 1985 & 1986) use force control instead of velocity. I would be interested to see which papers began to use the method for velocity control. – Mitchell Allain Feb 13 '17 at 19:04