eth-janishutz/eth-summaries
1
0
Fork 0
mirror of https://github.com/janishutz/eth-summaries.git synced 2026-03-14 04:40:07 +01:00
Code Issues Packages Projects Releases Wiki Activity

[AMR] Continue

Browse Source
This commit is contained in:
Janis Hutz
2026-03-13 17:24:06 +01:00
parent d7d75c789c
commit 253335df2f
2 changed files with 5 additions and 2 deletions
Download Patch File Download Diff File Expand all files Collapse all files

BIN
electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf
View File

Binary file not shown.

7
electives/others/amr/parts/01_kinematics/03_temporal-models.tex
View File

@@ -1,3 +1,6 @@
\subsection{Temporal Models} \subsection{Temporal Models}
Often use cont. time n.-lin. system of ODE $\dot{\vec{x}} = \vec{f}_C(\vec{x}(t), \vec{u}(t))$, with measurements $\vec{z}(t) = \vec{h}(\vec{x}(t))$. Often use cont. time n.-lin. system of ODE $\dot{\vec{x}} = \vec{f}_C(\vec{x}(t), \vec{u}(t))$, with measurements $\vec{z}(t) = \vec{h}(\vec{x}(t)) + \vec{v}(t)$.
Need linearised (around $\vec{f}_C(\vec{\overline{x}}, \vec{\overline{y}}) = 0$, at \bi{equilibrium}) Need linearised (around $\vec{f}_C(\vec{\overline{x}}, \vec{\overline{y}}) = 0$, at \bi{equilibrium}):\\
$\delta \vec{\dot{x}}(t) = \vec{f}_C(\vec{\overline{x}}, \vec{\overline{u}}) + \mat{F}_C \delta \vec{x}(t) + \mat{G}_C \delta \vec{u}(t) + \mat{L}_C \vec{w}(t)$\\
$\delta \vec{z}(t) = \mat{H} \delta \vec{x}(t) + \vec{v}(t)$.
Herein, $\mat{H}$ is measurements, $\mat{F}_C$ system, $\mat{G}$ input gain, $\vec{w}$ process noise, $\vec{v}$ measurement noise