Why is analysis required to study robotics?

I am studying Informatics and I am interested in doing a Masters in Robotics and I was checking out some unis and their courses and I saw that Robotics contains analysis and a lot of math.

Why is that?

• What sounds quite strange to me is that you had to reach that level in your study to understand that math is very very important. – Ugo Pattacini Dec 28 '14 at 13:04

Math is the way that roboticists translate our understanding of the world into something that a computer can understand. Since this is not how humans do it, this requires a lot of rather difficult math. How would you tell a computer what a pencil is? How does that description change if the pencil is rotated?

Robot control also needs a lot of math. If I move this shoulder joint by 5 degrees how much does that move the hand? If I the robot sees the world through a camera and I want the robot to move an object 5 pixels to the right, how much do I need to move each joint? If the object weighs 5 kg how much torque do I need on the motors to hold it? How do I make sure this works even if I measured wrong and the object is really 6kg?

Also, robots have to deal with a lot of uncertainty. The sensors it uses to "see" the world have a lot of random noise so all the algorithms need to somehow model this noise so the robot can react properly. This involves a lot of probability theory.

Finally, since it's not possible to test every environment you have to use math to prove that your algorithms will always work.

The short answer is that learning robotics is easier with the math than without.

Here are a few areas of robotics and the field of mathematics that make them manageable:

• Measuring data from sensors, with some level of uncertainty: statistics
• Solving problems through reasoning: formal logic
• Kinematics: linear algebra
• Control theory: calculus
• Algorithms: theory of computation, combinatorics
• Mechanical design: physics
• Sonar design: acoustics
• Cooperative robotics, path planning: graph theory

This is a very incomplete list.

Being able to predict or explain why a system works the way it does is very difficult without the mathematical language to describe it. The ideas are complicated, and you'd be hard pressed to find a more understandable way to communicate all but the simplest ideas in robotics without a mathematical language to rely on. (Not to mention that it's a more objective process to simplify mathematical equations than an english description of the same system.)

You may find that studying robotics will make it easier to learn the math, because it will give you a practical application for what's ordinarily just a bunch of theory.