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M  Presentations/ERLM/bouncing_ball_hybrid.png

M  Presentations/ERLM/bouncing_ball_hybrid.py

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
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Dane Sabo 2025-11-29 22:02:14 -05:00
parent e75afe3f8b
commit e19888ad07
12 changed files with 529 additions and 125 deletions
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Presentations/ERLM/bouncing_ball_hybrid.png
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95
Presentations/ERLM/bouncing_ball_hybrid.py
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@ -200,13 +200,13 @@ def plot_simulation(t, y, states, ball, show_phase=True):
state_numeric = np.array([1 if s == "free_fall" else 2 for s in states]) state_numeric = np.array([1 if s == "free_fall" else 2 for s in states])
if show_phase: if show_phase:
fig, axes = plt.subplots(2, 2, figsize=(14, 10)) fig, axes = plt.subplots(2, 1, figsize=(8, 10))
else: else:
fig, axes = plt.subplots(2, 1, figsize=(12, 8)) fig, axes = plt.subplots(2, 1, figsize=(12, 8))
axes = axes.reshape(-1, 1) axes = axes.reshape(-1, 1)
# Plot 1: Position vs Time # Plot 1: Position vs Time
ax1 = axes[0, 0] if show_phase else axes[0] ax1 = axes[0] if show_phase else axes[0]
scatter = ax1.scatter(t, y[:, 0], c=state_numeric, s=1, cmap="coolwarm", alpha=0.6) scatter = ax1.scatter(t, y[:, 0], c=state_numeric, s=1, cmap="coolwarm", alpha=0.6)
ax1.axhline( ax1.axhline(
y=ball.r, y=ball.r,
@ -229,35 +229,9 @@ def plot_simulation(t, y, states, ball, show_phase=True):
ax1.grid(True, alpha=0.3) ax1.grid(True, alpha=0.3)
ax1.legend(fontsize=9) ax1.legend(fontsize=9)
# Add colorbar
cbar1 = plt.colorbar(scatter, ax=ax1)
cbar1.set_label("State", fontsize=10)
cbar1.set_ticks([1.33, 1.67])
cbar1.set_ticklabels(["Free Fall", "Spring-Damper"])
# Plot 2: Velocity vs Time
ax2 = axes[1, 0] if show_phase else axes[1]
scatter2 = ax2.scatter(t, y[:, 1], c=state_numeric, s=1, cmap="coolwarm", alpha=0.6)
# Mark transitions
for t_trans in ball.transition_times:
ax2.axvline(x=t_trans, color="green", linestyle=":", alpha=0.3, linewidth=1)
ax2.axhline(y=0, color="k", linestyle="--", linewidth=1, alpha=0.3)
ax2.set_xlabel("Time (s)", fontsize=11)
ax2.set_ylabel("Velocity (m/s)", fontsize=11)
ax2.set_title("Ball Velocity vs Time", fontsize=12, fontweight="bold")
ax2.grid(True, alpha=0.3)
# Add colorbar
cbar2 = plt.colorbar(scatter2, ax=ax2)
cbar2.set_label("State", fontsize=10)
cbar2.set_ticks([1.33, 1.67])
cbar2.set_ticklabels(["Free Fall", "Spring-Damper"])
if show_phase: if show_phase:
# Plot 3: Vector Field / Phase Portrait # Plot 2: Vector Field / Phase Portrait
ax3 = axes[0, 1] ax2 = axes[1]
# Create vector field grid # Create vector field grid
pos_range = np.linspace(0, max(y[:, 0]) * 1.1, 15) pos_range = np.linspace(0, max(y[:, 0]) * 1.1, 15)
@ -286,59 +260,22 @@ def plot_simulation(t, y, states, ball, show_phase=True):
damping_force = ball.c * vel_val damping_force = ball.c * vel_val
dVel[i, j] = (spring_force - damping_force - ball.m * ball.g) / ball.m dVel[i, j] = (spring_force - damping_force - ball.m * ball.g) / ball.m
# Plot vector field # Plot vector field with much smaller scale
ax3.quiver(Pos, Vel, dPos, dVel, alpha=0.4, color='gray', scale=50) ax2.quiver(Pos, Vel, dPos, dVel, alpha=0.3, color='gray', scale=300, width=0.003)
# Plot trajectory # Plot trajectory
scatter3 = ax3.scatter( scatter2 = ax2.scatter(
y[:, 0], y[:, 1], c=state_numeric, s=1, cmap="coolwarm", alpha=0.6 y[:, 0], y[:, 1], c=state_numeric, s=2, cmap="coolwarm", alpha=0.7
) )
ax3.axvline( ax2.axvline(
x=ball.r, color="k", linestyle="--", label=f"Contact threshold", linewidth=1 x=ball.r, color="k", linestyle="--", label=f"Contact threshold", linewidth=1.5
) )
ax3.axhline(y=0, color="gray", linestyle="-", linewidth=1, alpha=0.5) ax2.axhline(y=0, color="gray", linestyle="-", linewidth=1, alpha=0.5)
ax3.set_xlabel("Position (m)", fontsize=11) ax2.set_xlabel("Position (m)", fontsize=11)
ax3.set_ylabel("Velocity (m/s)", fontsize=11) ax2.set_ylabel("Velocity (m/s)", fontsize=11)
ax3.set_title("Vector Field & Phase Portrait", fontsize=12, fontweight="bold") ax2.set_title("Vector Field & Phase Portrait", fontsize=12, fontweight="bold")
ax3.grid(True, alpha=0.3) ax2.grid(True, alpha=0.3)
ax3.legend(fontsize=9) ax2.legend(fontsize=9)
# Add colorbar
cbar3 = plt.colorbar(scatter3, ax=ax3)
cbar3.set_label("State", fontsize=10)
cbar3.set_ticks([1.33, 1.67])
cbar3.set_ticklabels(["Free Fall", "Spring-Damper"])
# Plot 4: Energy
ax4 = axes[1, 1]
# Calculate energies
KE = 0.5 * ball.m * y[:, 1] ** 2
PE = ball.m * ball.g * y[:, 0]
# Elastic potential energy when compressed
elastic_PE = np.zeros_like(y[:, 0])
for i, (pos, state) in enumerate(zip(y[:, 0], states)):
if state == "spring_damper" and pos < ball.r:
compression = ball.r - pos
elastic_PE[i] = 0.5 * ball.k * compression**2
total_E = KE + PE + elastic_PE
ax4.plot(t, KE, label="Kinetic", linewidth=1.5, alpha=0.7)
ax4.plot(t, PE, label="Gravitational PE", linewidth=1.5, alpha=0.7)
ax4.plot(t, elastic_PE, label="Elastic PE", linewidth=1.5, alpha=0.7)
ax4.plot(t, total_E, label="Total", linewidth=2, color="black", linestyle="--")
# Mark transitions
for t_trans in ball.transition_times:
ax4.axvline(x=t_trans, color="green", linestyle=":", alpha=0.3, linewidth=1)
ax4.set_xlabel("Time (s)", fontsize=11)
ax4.set_ylabel("Energy (J)", fontsize=11)
ax4.set_title("Energy Components", fontsize=12, fontweight="bold")
ax4.grid(True, alpha=0.3)
ax4.legend(fontsize=9)
plt.tight_layout() plt.tight_layout()
return fig return fig

28
Presentations/ERLM/main.aux
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42
Presentations/ERLM/main.fls
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\begin{frame}{Finally, we will build continuous controllers to move between \begin{frame}{Finally, we will build continuous controllers to move between
discrete states} discrete states}
\begin{columns}
\begin{column}{0.5\textwidth}
\includegraphics[height=0.7\textheight]{bouncing_ball_hybrid.png}
\end{column}
\begin{column}{0.5\textwidth}
\only<2>{
\begin{alertblock}{Key Challenge}
\small
Verify continuous control behavior across discrete mode transitions
\end{alertblock}
}
\only<3->{
\begin{block}{Key Challenge}
\small
Verify continuous control behavior across discrete mode transitions
\end{block}
}
\vspace{0.3cm}
\only<3>{
\begin{alertblock}{Reachable Set}
\small
$\mathcal{R}(t) = \{x(t) \mid x(0) \in X_0, \dot{x} = f(x)\}$
\end{alertblock}
}
\only<4->{
\begin{block}{Reachable Set}
\small
$\mathcal{R}(t) = \{x(t) \mid x(0) \in X_0, \dot{x} = f(x)\}$
\end{block}
}
\vspace{0.3cm}
\only<4>{
\begin{alertblock}{Barrier Certificate}
\small
$B(x) > 0 \land \nabla B \cdot f(x) \leq 0 \implies x \in \text{Safe}$
\end{alertblock}
}
\end{column}
\end{columns}
\end{frame} \end{frame}
\begin{frame}{Verified autonomous controllers can be created by building this \begin{frame}{Verified autonomous controllers can be created by building this
chain of proof of correctness} chain of proof of correctness}
\begin{enumerate}
\item<1-> \alert<1>{Formalize regulatory procedures into FRET specifications and translate to Linear Temporal Logic (LTL)}
\item<2-> \alert<2>{Synthesize discrete automata from LTL using reactive synthesis}
\item<3-> \alert<3>{Design continuous controllers for each discrete mode and verify safety across mode transitions using barrier certificates and reachability analysis}
\end{enumerate}
\vspace{1cm}
\onslide<4>{
\begin{center}
\large
\textbf{Result: Complete hybrid autonomous system\\
with correctness guarantees by construction}
\end{center}
}
\end{frame} \end{frame}

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Presentations/ERLM/slides/5_Metrics_of_Success.tex
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\begin{frame}{Success is measured through Technology Readiness Level advancement}
\begin{columns}
\begin{column}{0.45\textwidth}
\begin{block}{Why TRLs?}
\small
Bridge gap between academic proof-of-concept and practical deployment
\begin{itemize}
\item[] Academic metrics $\rightarrow$ cannot capture feasibility
\item[] Empirical metrics $\rightarrow$ cannot demonstrate rigor
\item[] TRLs measure both simultaneously
\end{itemize}
\end{block}
\end{column}
\begin{column}{0.55\textwidth}
\begin{block}{Progression Path}
\small
\textbf{Current: TRL 2-3}\\
Fundamental principles established
\vspace{0.3cm}
\textbf{Target: TRL 5}\\
Lab testing in relevant environment
\end{block}
\end{column}
\end{columns}
\end{frame}
\begin{frame}{TRL advancement requires achieving three validation milestones}
\begin{enumerate}
\item<1-> \alert<1>{\textbf{TRL 3: Critical Function \& Proof of Concept}}
\begin{itemize}
\item[] Each component works in isolation
\item[] Specifications pass realizability analysis
\item[] At least one continuous controller with reachability proof
\end{itemize}
\item<2-> \alert<2>{\textbf{TRL 4: Integrated Components in Simulation}}
\begin{itemize}
\item[] Complete integrated hybrid controller
\item[] All mode transitions verified
\item[] Zero safety violations across multiple runs
\end{itemize}
\item<3-> \alert<3>{\textbf{TRL 5: Testing in Relevant Environment}}
\begin{itemize}
\item[] Hardware-in-the-loop on Emerson Ovation
\item[] Autonomous startup sequences via HIL
\item[] Off-nominal scenarios handled correctly
\item[] Formal verification remains valid on hardware
\end{itemize}
\end{enumerate}
\end{frame}

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\begin{frame}{Four primary risks with clear mitigation and contingency plans}
\begin{enumerate}
\item<1-> \alert<1>{\textbf{Computational Tractability of Synthesis}}
\begin{itemize}
\item[] \textit{Risk:} Synthesis times exceed project timeline
\item[] \textit{Indicator:} $>$24hr for simplified procedures
\item[] \textit{Contingency:} Reduce to minimal viable startup sequence
\item[] \textit{Mitigation:} HPC resources, compositional verification
\end{itemize}
\item<2-> \alert<2>{\textbf{Discrete-Continuous Interface Complexity}}
\begin{itemize}
\item[] \textit{Risk:} Boolean guards cannot map to continuous dynamics
\item[] \textit{Indicator:} No barrier certificates exist for transitions
\item[] \textit{Contingency:} Restrict to polytopic invariants
\item[] \textit{Mitigation:} Design controllers with transitions as constraints
\end{itemize}
\item<3-> \alert<3>{\textbf{Procedure Formalization Completeness}}
\begin{itemize}
\item[] \textit{Risk:} Procedures lack precision for autonomous control
\item[] \textit{Indicator:} Multiple valid interpretations, operator judgment
\item[] \textit{Contingency:} Document gaps as research contribution
\item[] \textit{Mitigation:} Early analysis with domain experts
\end{itemize}
\item<4-> \alert<4>{\textbf{Hardware-in-the-Loop Integration}}
\begin{itemize}
\item[] \textit{Risk:} Real-time constraints incompatible with hardware
\item[] \textit{Indicator:} Communication dropouts, missed deadlines
\item[] \textit{Contingency:} Software-in-the-loop with timing analysis (TRL 4)
\item[] \textit{Mitigation:} Early integration testing, ARCADE infrastructure
\end{itemize}
\end{enumerate}
\end{frame}
\begin{frame}{Staged structure ensures partial success yields valuable results}
\begin{columns}
\begin{column}{0.5\textwidth}
\begin{block}{Early Detection}
\small
Each risk has specific indicators for early warning
\begin{itemize}
\item[] Quarterly assessment of progress
\item[] Data-driven plan revision only when assumptions invalidated
\end{itemize}
\end{block}
\end{column}
\begin{column}{0.5\textwidth}
\begin{block}{Research Value}
\small
Even contingency outcomes contribute knowledge
\begin{itemize}
\item[] Identifying barriers is itself valuable
\item[] Clear pathway for future work
\item[] Publishable results at each stage
\end{itemize}
\end{block}
\end{column}
\end{columns}
\vspace{1cm}
\begin{center}
\textbf{Contingency plans preserve core methodology\\
while adjusting scope to maintain feasibility}
\end{center}
\end{frame}