[AMR] Week2: Done

electives/others/amr/autonomous-mobile-robots-cheatsheet.tex

@@ -35,12 +35,17 @@
 \end{center}
 
 
+% TODO: Graphics
 \section{Introduction}
 \input{parts/00_basics/00_probability.tex}
 \input{parts/00_basics/01_measurement-models.tex}
+\input{parts/00_basics/02_trigonometry.tex}
 
 \section{Locomotion \& Kinematics}
 \input{parts/01_kinematics/00_intro.tex}
+\input{parts/01_kinematics/01_forward.tex}
+\input{parts/01_kinematics/02_inverse.tex}
+% \input{parts/01_kinematics/}
 
 
 \end{document}

electives/others/amr/parts/00_basics/02_trigonometry.tex

@@ -0,0 +1,3 @@
+\subsection{Trigonometry}
+% TODO: Cosine rule (at least), probably also sine rule.
+% TODO: Add convenient results (such as cos2 + sin2 = 1)

electives/others/amr/parts/01_kinematics/01_forward.tex

@@ -0,0 +1,8 @@
+\subsection{Forward Kinematics (FK)}
+$T_{WB_n}(\theta) = \mat{T}_{WB_0} \mat{T}_{B_0B_1}(\theta_1) \cdots \mat{T}_{B_{n - 1}B_n}(\theta_n)$.\\
+For 2R system: ${_W}\vec{t}_{WE} = \begin{bmatrix}
+    L_1 \cos(\theta_1) + L_2 \cos(\theta_1 + \theta_2)\\
+    L_1 \sin(\theta_1) + L_2 \sin(\theta_1 + \theta_2)
+\end{bmatrix}$\\
+With workspace (pos) $W$ for $\theta_1, \theta_2 \in [-\pi, \pi]$
+% TODO: Example? (w02s42 possibly)

electives/others/amr/parts/01_kinematics/02_inverse.tex

@@ -0,0 +1,15 @@
+\subsection{Inverse Kinematics (IK)}
+\begin{wrapfigure}[10]{r}{0.4\columnwidth}
+    \includegraphics[width=0.4\columnwidth]{assets/inverse-kinematics.png}
+\end{wrapfigure}
+Option: Solve Forward Kinematics for angles.\\
+Better: Law of cosine with polar coordinates. Compute angle using cosine rule,\\
+$\theta_1 = \phi \pm \alpha$, $\theta_2 = \pm(\pi - \beta)$
+
+(Positive for {\color{ForestGreen} Elbow Down}, Negative for {\color{red} Elbow Up})
+
+Extension to 6R:
+1. Waist: spherical coords (2 sol.)\\
+2. 2 sols from 2R for shoulder + elbow\\
+3. Solve for wrist joints (no influence on pos)
+