eth-janishutz/eth-summaries
1
0
Fork 0
mirror of https://github.com/janishutz/eth-summaries.git synced 2026-07-27 21:29:09 +02:00
Code Issues Packages Projects Releases Wiki Activity

[AMR] Reduce font size, some additions

Browse Source
This commit is contained in:
janishutz
2026-07-18 11:03:37 +02:00
parent 89009ef7d3
commit 71dd2817f4
6 changed files with 26 additions and 15 deletions
Download Patch File Download Diff File Expand all files Collapse all files
electives/amr/parts/01_kinematics/01_forward.tex
+6 -5
View File
@@ -1,15 +1,16 @@
\subsection{Forward Kinematics (FK)}
$\mat{T}_{WB_n}(\vec{\theta}) = \mat{T}_{WB_0} \mat{T}_{B_0B_1}(\theta_1) \cdots \mat{T}_{B_{n - 1}B_n}(\theta_n)$.\\
For 2R system:
${_W}\vec{t}_{WE} =$
$\mat{T}_{WB_n}(\vec{\theta}) = \mat{T}_{WB_0} \mat{T}_{B_0B_1}(\theta_1) \cdots \mat{T}_{B_{n - 1}B_n}(\theta_n)$.
For 2R system: ${_W}\vec{t}_{WE} =$
{\scriptsize
$ \begin{bmatrix}
L_1 \cos(\theta_1) + L_2 \cos(\theta_1 + \theta_2) \\
L_1 \sin(\theta_1) + L_2 \sin(\theta_1 + \theta_2)
\end{bmatrix}$\\
}
Similar for $n$R sys (more angles). Wspc $W$ $\theta_1, \theta_2 \in [-\pi, \pi]$.
Last dim may be sum of angles. Jacobian: see \ref{sec:ms-lin}
Workspace $W$: $\theta_1, \theta_2 \in [-\pi, \pi]$.
Similar for $n$R sys (more angles, more lengths).
For 2D move in 3D space, last dim is sum of angles (or equiv). \bi{Jacobian}: see \ref{sec:ms-lin}
\shortdefinition[Singularity] Loss of deg of Freed. $\det(\mat{J}(\vec{\theta})) = 0$
% TODO: Determinant computation
electives/amr/parts/01_kinematics/06_wheeled-robot.tex
+9 -4
View File
@@ -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}