State space and control space

Question

I would like to know the difference between state space and control space in relation to motion planning. I would like a simpler explanation.

Answer 1

The state space is the space of possible values that the state can take. For any given system it depends on which variables you are taking into account. For instance it is common to consider the 2D position $(x, y)$ and the orientation $\theta$ of the system. For this example the state space consists of three dimensions where $x$ and $y$ could conceivable come from either $\mathbb{R}$ or some bounded subset depending on the problem and $\theta \in [0, 2\pi)$.

Similarly the control space consists of the possible control values that can be applied to the system. For example if you using torque control on a pendulum then it would be the torques your motor can produce. Usually a bounded, and in practice a discrete, subset of $\mathbb{R}$.