From e75afe3f8b5dcfc70024e200557f3f73d3049673 Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Sat, 29 Nov 2025 19:04:25 -0500 Subject: [PATCH] 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 | 36 ++++++- .../images/4_research_approach/procedure.png | Bin 0 -> 158772 bytes Presentations/ERLM/main.aux | 24 ++--- Presentations/ERLM/main.fdb_latexmk | 25 ++++- Presentations/ERLM/main.fls | 36 +++++++ Presentations/ERLM/main.log | 101 +++++++++++++----- Presentations/ERLM/main.nav | 22 ++-- Presentations/ERLM/main.pdf | Bin 1624431 -> 1767385 bytes Presentations/ERLM/main.synctex.gz | Bin 44834 -> 47763 bytes .../ERLM/slides/4_Research_Approach.tex | 71 +++++++++++- 10 files changed, 255 insertions(+), 60 deletions(-) create mode 100644 Presentations/ERLM/images/4_research_approach/procedure.png diff --git a/Presentations/ERLM/bouncing_ball_hybrid.py b/Presentations/ERLM/bouncing_ball_hybrid.py index bd6c0501a..9e6a81204 100644 --- a/Presentations/ERLM/bouncing_ball_hybrid.py +++ b/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) 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z9Ysc6*^xe;>9YVo&Npk?+kk5TT1nsM*ZT6}^EYUl&%LOjnu-kXyYrw^eQ&p&_J^U8 z$W!3%q^th)ajgF7$B^r4>(8_G!^n!qDx6oOnNerQt3G#Uz+12Ti{snX$NT1bQo!y0 z=gi`%k6SGZz2H0P^Tnr!-wi1J)~6eVw-3KAnj`ODUBJdgwLJ_q*HtY~YzzjbYIc?drBvvj>plE%CWLSJot YTHlRq|8+I8{Dh$4@lw`G9|7wB18IHGJOBUy diff --git a/Presentations/ERLM/slides/4_Research_Approach.tex b/Presentations/ERLM/slides/4_Research_Approach.tex index c7f3d7732..376ff9c00 100644 --- a/Presentations/ERLM/slides/4_Research_Approach.tex +++ b/Presentations/ERLM/slides/4_Research_Approach.tex @@ -23,12 +23,81 @@ \begin{frame}{First, we will formalize written procedures into logical statements} - + + \begin{columns} + \begin{column}{0.33\textwidth} + \includegraphics[width=\textwidth]{images/4_research_approach/procedure.png} + \end{column} + + \begin{column}{0.33\textwidth} + \only<2>{ + \begin{alertblock}{FRET Specification} + \scriptsize + \texttt{INITIAL\_CONDITIONS shall satisfy:} + \begin{itemize} + \item[] \texttt{mode = MODE\_5} + \item[] \texttt{k\_eff < 0.99} + \item[] \texttt{power = 0} + \item[] \texttt{t\_avg < 200} + \item[] \texttt{...} + \end{itemize} + \end{alertblock} + } + + \only<3->{ + \begin{block}{FRET Specification} + \scriptsize + \texttt{INITIAL\_CONDITIONS shall satisfy:} + \begin{itemize} + \item[] \texttt{mode = MODE\_5} + \item[] \texttt{k\_eff < 0.99} + \item[] \texttt{power = 0} + \item[] \texttt{t\_avg < 200} + \item[] \texttt{...} + \end{itemize} + \end{block} + } + \end{column} + + \begin{column}{0.33\textwidth} + \only<3>{ + \begin{alertblock}{LTL Formula} + \scriptsize + \texttt{$\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