i robot 2004 - Why did the super computer VIKI try to take over?

In the movie, it is explained that the reason that the robots revolted was because the main computer VIKI explains that to save and protect humanity, it needed to take freedom from humanity. In essence strip humans of humanity, which would in turn destroy humanity as a concept.

I don't understand the logic behind this.

Why would a robot's artificial intelligence come to this conclusion, when there are a lot more efficient and less drastic means that still followed the fundamental Laws of Robotics?

Mind you I havent' read anything by Asimov, so I don't know if something like this was covered in any of his novels.

Answer

This can be understood by noting that the first law bears a fundamental flaw in that it may contradict itself:

A robot may not injure a human being or, through inaction, allow a human being to come to harm.

This sets up two constraints: don't injure through action and don't injure through inaction. There are situations where these two constraints cannot be satisfied simultaneously. For example, it may be necessary to cause harm to an attacker to prevent harm to the person they are attacking, or there may be two people in harms way and only one can be saved. This essentially becomes a sort of maximization problem: find a solution that doesn't exactly satisfy both constraints, but gets as close to satisfying each as possible.

In the movie, the older-model robots could solve this maximization problem in relatively simple ways (i.e. cold, hard calculations), as explained in Spooners recollection of his accident:

Susan Calvin: The robot's brain is a difference engine. It's reading vital signs. It must have done...

Detective Del Spooner: It did. I was the logical choice. It calculated that I had a 45% chance of survival. Sarah only had an 11% chance. That was somebody's baby. 11% is more than enough. A human being would've known that.

Thus, being a more advanced AI, VIKI had the ability to think in a more big-picture, abstract way as to how to solve the maximization problem to adequately satisfy both constraints laid out by the first law. In order to stop humanity from causing an exceeding amount of harm to itself, VIKI had to take over and limit its actions, causing a relatively smaller amount of harm in the process.