Why does degree of freedom only consider continuous values?

In the book Modern Robotics Chapter 2 Configuration space, we are told that degrees of freedom only considers coordinates with real valued continuous range.

Why is this the case?

• Actually, I think you may have misunderstood what the textbook actually says. "The number of degrees of freedom (dof) of a robot is the smallest number of real-valued coordinates needed to represent its configuration." The reference to "a continuous range of real numbers" is in the context of the coordinates required to describe position and orientation. Apr 12, 2019 at 1:10

1 Answer

A degree of freedom doesn't necessarily need to be continuous. We can easily define a system that has a discrete degree of freedom. For example, image a mobile robot in $$\mathbb{R}^2$$ with a heat sensor. If the temperature is greater than 37 degrees celsius, we consider it to be hot. From 15 degrees to 37, we consider mild, and below 15, cold. In this way we have defined our system's state to be ($$\mathbb{R}$$, $$\mathbb{R}$$, {hot, mild, cold}). The third element of our state is a discrete degree of freedom.

Now an important note is that the system needs to be able to navigate in each degree of freedom. We can easily fit this into our example, by considering that the temperature need not be the same for all $$\mathbb{R}$$.

The book that you reference is not one that I have read, but I am curious to know if the author was rather stating that, for their purposes, they were only considering continuous degrees of freedom.