\subsection{Inverse Kinematics (IK)}
\begin{wrapfigure}[10]{r}{0.35\columnwidth}
    \includegraphics[width=0.35\columnwidth]{assets/inverse-kinematics.png}
\end{wrapfigure}
\bi{Option}: Solve FK for angles.\\
\bi{Better}: Law of cosine with polar coordinates. Compute angle using cosine rule,
$\theta_1 = \varphi \pm \alpha$, $\theta_2 = \pm(\pi - \beta)$
(Positive for {\color{ForestGreen} Elbow Down}, Neg. for {\color{red} Elbow Up})

\bi{Extension to 6R}:
1. Waist: spherical coords (2 sol.)\\
2. 2 sols from 2R for shoulder + elbow\\
3. Solve for wrist joints (no infl. on pos)

\bi{For Inv. velocity}: $\vec{\dot{\theta}} = J_S^{-1}(\vec{\theta}) {_W} \dot{\vec{t}}_{WE}$

% \shortdefinition[Denavit-Hartengerb (DH)] Serial chains
% \[
%     \mat{T}_{L_j L_{j + 1}} = \mat{T}^{R_z}(\theta_j) \mat{T}^{t_z}(d_j) \mat{T}^{t_x}(a_j) \mat{T}^{R_x}(\alpha_j)
% \]
% with $

\shortdefinition[Underactuated] workspace $<6$D; IK solvable

\shortdefinition[Overactuated] $\8$ IK sol; Reduced singularities; Num. sol.