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[AMR] Reduce font size, some additions

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janishutz
2026-07-18 11:03:37 +02:00
parent 89009ef7d3
commit 71dd2817f4
6 changed files with 26 additions and 15 deletions
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electives/amr/parts/01_kinematics/06_wheeled-robot.tex
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@@ -4,13 +4,18 @@
\end{wrapfigure}
\bi{Non-holonomic} systems \textbf{not integrable}, no inst. move in every direct.
\bi{Wheel constraints} $v_i = \omega_i r_i$
\bi{Wheel constraints} $v_i = \omega_i r_i$ ($r_i$ constraints)
\begin{itemize}
\item \textit{Driving straight} all $\vec{v}$ equal
\item \textit{Turning} Wheel axis must intersect the \bi{Instant Centre of Rotation} (ICR),
speeds: $v_i \div R_i = \Omega$ ($R_i$ = dist. wheel-ICR; $\Omega$: vehicle body rotation rate)
\item \textit{Turning} Wheel axis must intersect the \bi{Instant Centre of Rotation} (ICR) of vehicle,
speeds: $v_i \div R_i = \Omega$ ($R_i$ = dist. wheel-ICR; $\Omega$: vehicle rotation rate (around ICR))
\end{itemize}
Below: $\alpha$, $l$ pos in frame, $\beta$ rot at that pos ($z$-ax).
To compute $\vec{c}$ in $\vec{c} \cdot {_B}\vec{v}_{WB} = \omega$
(For multiple wheels, construct mat. from this)
$c_i = [\sin(\alpha + \beta) \div r, -\cos(\alpha + \beta) \div r, -\cos(\beta) \cdot l \div r]$
\bi{Maneuverability}
\begin{itemize}