[AMR] Add feedback loops

electives/amr/parts/00_basics/01_measurement-models.tex

@@ -4,3 +4,6 @@ $\vec{b}_C$ const bias, $\vec{b}$ time bias, $\mat{M}$ missal., $\vec{n} \sim \c
 
 \hl{Finding}: Is in $W$-frame: may need $\mat{T}_{BW}$ or $\mat{R}_{BW}$.
 Also see Sec.~\ref{sec:sensors}
+
+Feedback loop:
+\includegraphics[width=0.6\columnwidth]{assets/loop-main.png}

electives/amr/parts/01_kinematics/03_temporal-models.tex

@@ -5,7 +5,7 @@
 Model \bi{robot dyn} as \bi{Cont-time non-lin. system of ODE}:\\
 $\dot{\vec{x}} = \vec{f}_C(\vec{x}(t), \vec{u}(t), \vec{w}(t))$, measurement $\vec{z}(t) = \vec{h}(\vec{x}(t)) + \vec{v}(t)$.
 
-With: $\pardiff{t}\vec{x}(t) = f_C(\vec{x}(t), \vec{u}(t))$ the model for the robot state update and $\vec{h}(\vec{x}(t))$ the model for the measurements (e.g. for IMU)
+With: $\pardiff{t}\vec{x}(t) = \vec{f}_C(\vec{x}(t), \vec{u}(t))$ the model for the robot state update and $\vec{h}(\vec{x}(t))$ the model for the measurements (e.g. for IMU)
 
 \vspace{0.5mm}
 \hrule

electives/amr/parts/05_planning-control/00_feedback-control/03_mpc.tex

@@ -1,3 +1,9 @@
+
+Below feedback loops for PID and LQR
+
+\includegraphics[width=0.49\columnwidth]{assets/loop-pid.png}
+\includegraphics[width=0.5\columnwidth]{assets/loop-lqr.png}
+
 \subsection{MPC}
 \bi{Cost function} ($p(\vec{x}_N)$ \textit{terminal cost}, sum the \textit{stage cost})
 \[

electives/amr/parts/05_planning-control/01_motion-planning-exploration/03_rrt.tex

@@ -1,4 +1,3 @@
-\newpage
 \subsubsection{Rapidly-Exploring Random Tree (RRT)}
 \begin{algorithm}
     \small
@@ -27,6 +26,9 @@
         \EndProcedure
     \end{algorithmic}
 \end{algorithm}
+Notes: \texttt{nearestConfiguration} may be on edge, then edge is split;
+\texttt{stoppingConfiguration} returns furthest config $x_f$ on segment $x_n$ to $x$ that produces collision-free edge $(x_n, x_f)$
+
 Returns a collision-free path as graph. Need nearest neighbour search.
 Extension to RRT* to make path better:
 \begin{algorithm}

electives/amr/parts/05_planning-control/02_learning-to-act/02_reinforcement-learning.tex

@@ -26,3 +26,6 @@ $\varepsilon$ is prob. to act randomly, $1 - \varepsilon$ is prob. to act on pol
 Value-based (estimate val or $Q$-func and extract pol., e.g. Q-Learn),
 Actor-Critic (estim. val or $Q$ of curr. pol., improve pol., e.g. A3C, SAC),
 Policy-Gradient (diff. expect. reward w.r.t. params of policy network, e.g. REINFORCE)
+
+\includegraphics[width=0.5\columnwidth]{assets/loop-rl.png}
+\includegraphics[width=0.5\columnwidth]{assets/loop-drl.png}