Error as a State space

Question

I am reading the following research paper regarding Trajectory tracking of mobile robots.

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5415188

There are two things at the start of the paper that i do not understand.

1) The author derives equation(14) as the state space model of the system in which he considers the error as the state. Can anyone please elaborate on why he is using the error as the state space model of the system and not the Vx, Vy, and w(Omega, angular speed) of the robot.

2) Why does the author linearize the system around the reference trajectory?

Answer 1

FYI, most people (including myself) can't see that paper because we don't have IEEE memberships.

Based on your question, though, the error is often considered the state because that is what you really care about in control/estimation algorithms: you want to control the robot so the error is zero. This is true whether the reference trajectory is static or dynamic.

For 2), it's hard to say without looking at the paper, but the reference trajectory is a logical point of linearization because you assume that your controller is good and the robot is close the the reference trajectory. This way you can linearize and design controllers in advance, i.e. when you don't know the true state so the reference trajectory is the only information you can use.