Auto sync: 2025-11-29 19:04:25 (10 files changed)

M  Presentations/ERLM/bouncing_ball_hybrid.py

A  Presentations/ERLM/images/4_research_approach/procedure.png

M  Presentations/ERLM/main.aux

M  Presentations/ERLM/main.fdb_latexmk

M  Presentations/ERLM/main.fls

M  Presentations/ERLM/main.log

M  Presentations/ERLM/main.nav

M  Presentations/ERLM/main.pdf

Presentations/ERLM/bouncing_ball_hybrid.py

@@ -256,8 +256,40 @@ def plot_simulation(t, y, states, ball, show_phase=True):
     cbar2.set_ticklabels(["Free Fall", "Spring-Damper"])
 
     if show_phase:
-        # Plot 3: Phase Portrait
+        # Plot 3: Vector Field / Phase Portrait
         ax3 = axes[0, 1]
+
+        # Create vector field grid
+        pos_range = np.linspace(0, max(y[:, 0]) * 1.1, 15)
+        vel_range = np.linspace(min(y[:, 1]) * 1.1, max(y[:, 1]) * 1.1, 15)
+        Pos, Vel = np.meshgrid(pos_range, vel_range)
+
+        # Calculate vector field
+        dPos = np.zeros_like(Pos)
+        dVel = np.zeros_like(Vel)
+
+        for i in range(Pos.shape[0]):
+            for j in range(Pos.shape[1]):
+                pos_val = Pos[i, j]
+                vel_val = Vel[i, j]
+
+                # Determine which dynamics to use
+                if pos_val > ball.r:
+                    # Free fall dynamics
+                    dPos[i, j] = vel_val
+                    dVel[i, j] = -ball.g
+                else:
+                    # Spring-damper dynamics
+                    dPos[i, j] = vel_val
+                    compression = ball.r - pos_val
+                    spring_force = ball.k * compression
+                    damping_force = ball.c * vel_val
+                    dVel[i, j] = (spring_force - damping_force - ball.m * ball.g) / ball.m
+
+        # Plot vector field
+        ax3.quiver(Pos, Vel, dPos, dVel, alpha=0.4, color='gray', scale=50)
+
+        # Plot trajectory
         scatter3 = ax3.scatter(
             y[:, 0], y[:, 1], c=state_numeric, s=1, cmap="coolwarm", alpha=0.6
         )
@@ -267,7 +299,7 @@ def plot_simulation(t, y, states, ball, show_phase=True):
         ax3.axhline(y=0, color="gray", linestyle="-", linewidth=1, alpha=0.5)
         ax3.set_xlabel("Position (m)", fontsize=11)
         ax3.set_ylabel("Velocity (m/s)", fontsize=11)
-        ax3.set_title("Phase Portrait", fontsize=12, fontweight="bold")
+        ax3.set_title("Vector Field & Phase Portrait", fontsize=12, fontweight="bold")
         ax3.grid(True, alpha=0.3)
         ax3.legend(fontsize=9)
 

Presentations/ERLM/main.aux

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Presentations/ERLM/main.nav

@@ -10,16 +10,16 @@
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Presentations/ERLM/slides/4_Research_Approach.tex

@@ -23,12 +23,81 @@
 
 \begin{frame}{First, we will formalize written procedures into logical
   statements}
-  
+
+  \begin{columns}
+    \begin{column}{0.33\textwidth}
+      \includegraphics[width=\textwidth]{images/4_research_approach/procedure.png}
+    \end{column}
+
+    \begin{column}{0.33\textwidth}
+      \only<2>{
+        \begin{alertblock}{FRET Specification}
+        \scriptsize
+        \texttt{INITIAL\_CONDITIONS shall satisfy:}
+        \begin{itemize}
+          \item[] \texttt{mode = MODE\_5}
+          \item[] \texttt{k\_eff < 0.99}
+          \item[] \texttt{power = 0}
+          \item[] \texttt{t\_avg < 200}
+          \item[] \texttt{...}
+        \end{itemize}
+      \end{alertblock}
+      }
+
+      \only<3->{
+        \begin{block}{FRET Specification}
+        \scriptsize
+        \texttt{INITIAL\_CONDITIONS shall satisfy:}
+        \begin{itemize}
+          \item[] \texttt{mode = MODE\_5}
+          \item[] \texttt{k\_eff < 0.99}
+          \item[] \texttt{power = 0}
+          \item[] \texttt{t\_avg < 200}
+          \item[] \texttt{...}
+        \end{itemize}
+      \end{block}
+      }
+    \end{column}
+
+    \begin{column}{0.33\textwidth}
+      \only<3>{
+        \begin{alertblock}{LTL Formula}
+          \scriptsize
+          \texttt{$\Box$ (initial $\rightarrow$ (}
+          \begin{itemize}
+            \item[] \texttt{mode = MODE\_5 $\land$}
+            \item[] \texttt{k\_eff < 0.99 $\land$}
+            \item[] \texttt{power = 0 $\land$}
+            \item[] \texttt{t\_avg < 200 $\land$}
+            \item[] \texttt{...))}
+          \end{itemize}
+        \end{alertblock}
+      }
+    \end{column}
+  \end{columns}
+
 \end{frame}
 
 \begin{frame}{Second, we will use the logical formulae to generate discrete
   automata}
 
+  \centering
+  \begin{tikzpicture}[node distance=2cm]
+    % Blocks
+    \node[draw, rectangle, minimum width=3cm, minimum height=1.5cm, align=center, fill=blue!20] (ltl) {LTL\\Specification};
+    \node[draw, rectangle, minimum width=3cm, minimum height=1.5cm, align=center, fill=blue!20, right=of ltl] (game) {Game\\Graph};
+    \node[draw, rectangle, minimum width=3cm, minimum height=1.5cm, align=center, fill=blue!20, right=of game] (automata) {Discrete\\Automata};
+
+    % Arrows
+    \draw[->, thick] (ltl) -- (game);
+    \draw[->, thick] (game) -- (automata);
+
+    % Curly bracket
+    \draw[decorate, decoration={brace, amplitude=10pt, mirror}, thick]
+      ([yshift=-1cm]ltl.south west) -- ([yshift=-1cm]automata.south east)
+      node[midway, below=0.5cm] {\textbf{Reactive Synthesis}};
+  \end{tikzpicture}
+
 \end{frame}
 
 \begin{frame}{Finally, we will build continuous controllers to move between