# Motion Model With Maps

tags
Velocity Motion Model, Odometry Motion Model

Often, we are given map $$m$$ of the environment, giving us further information about the robot pose $$x_t$$. In general,

$$p\left(x_{t} | u_{t}, x_{t-1}\right) \neq p\left(x_{t} | u_{t}, x_{t-1}, m\right)$$

And the map-based motion model should give better results. Computing this motion model in closed form is difficult. An approximation via factorization works well where the distance $$x_{t-1}$$ and $$x_t$$ is small.

$$p\left(x_{t} | u_{t}, x_{t-1}, m\right)=\eta p\left(x_{t} | u_{t}, x_{t-1}\right) p\left(x_{t} | m\right)$$

Icon by Laymik from The Noun Project. Website built with ♥ with Org-mode, Hugo, and Netlify.