Auto sync: 2025-11-29 22:02:14 (12 files changed)
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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@ -200,13 +200,13 @@ def plot_simulation(t, y, states, ball, show_phase=True):
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state_numeric = np.array([1 if s == "free_fall" else 2 for s in states])
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if show_phase:
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fig, axes = plt.subplots(2, 2, figsize=(14, 10))
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fig, axes = plt.subplots(2, 1, figsize=(8, 10))
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else:
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fig, axes = plt.subplots(2, 1, figsize=(12, 8))
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axes = axes.reshape(-1, 1)
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# Plot 1: Position vs Time
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ax1 = axes[0, 0] if show_phase else axes[0]
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ax1 = axes[0] if show_phase else axes[0]
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scatter = ax1.scatter(t, y[:, 0], c=state_numeric, s=1, cmap="coolwarm", alpha=0.6)
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ax1.axhline(
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y=ball.r,
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@ -229,35 +229,9 @@ def plot_simulation(t, y, states, ball, show_phase=True):
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ax1.grid(True, alpha=0.3)
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ax1.legend(fontsize=9)
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# Add colorbar
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cbar1 = plt.colorbar(scatter, ax=ax1)
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cbar1.set_label("State", fontsize=10)
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cbar1.set_ticks([1.33, 1.67])
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cbar1.set_ticklabels(["Free Fall", "Spring-Damper"])
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# Plot 2: Velocity vs Time
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ax2 = axes[1, 0] if show_phase else axes[1]
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scatter2 = ax2.scatter(t, y[:, 1], c=state_numeric, s=1, cmap="coolwarm", alpha=0.6)
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# Mark transitions
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for t_trans in ball.transition_times:
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ax2.axvline(x=t_trans, color="green", linestyle=":", alpha=0.3, linewidth=1)
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ax2.axhline(y=0, color="k", linestyle="--", linewidth=1, alpha=0.3)
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ax2.set_xlabel("Time (s)", fontsize=11)
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ax2.set_ylabel("Velocity (m/s)", fontsize=11)
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ax2.set_title("Ball Velocity vs Time", fontsize=12, fontweight="bold")
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ax2.grid(True, alpha=0.3)
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# Add colorbar
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cbar2 = plt.colorbar(scatter2, ax=ax2)
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cbar2.set_label("State", fontsize=10)
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cbar2.set_ticks([1.33, 1.67])
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cbar2.set_ticklabels(["Free Fall", "Spring-Damper"])
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if show_phase:
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# Plot 3: Vector Field / Phase Portrait
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ax3 = axes[0, 1]
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# Plot 2: Vector Field / Phase Portrait
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ax2 = axes[1]
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# Create vector field grid
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pos_range = np.linspace(0, max(y[:, 0]) * 1.1, 15)
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@ -286,59 +260,22 @@ def plot_simulation(t, y, states, ball, show_phase=True):
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damping_force = ball.c * vel_val
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dVel[i, j] = (spring_force - damping_force - ball.m * ball.g) / ball.m
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# Plot vector field
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ax3.quiver(Pos, Vel, dPos, dVel, alpha=0.4, color='gray', scale=50)
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# Plot vector field with much smaller scale
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ax2.quiver(Pos, Vel, dPos, dVel, alpha=0.3, color='gray', scale=300, width=0.003)
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# Plot trajectory
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scatter3 = ax3.scatter(
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y[:, 0], y[:, 1], c=state_numeric, s=1, cmap="coolwarm", alpha=0.6
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scatter2 = ax2.scatter(
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y[:, 0], y[:, 1], c=state_numeric, s=2, cmap="coolwarm", alpha=0.7
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)
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ax3.axvline(
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x=ball.r, color="k", linestyle="--", label=f"Contact threshold", linewidth=1
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ax2.axvline(
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x=ball.r, color="k", linestyle="--", label=f"Contact threshold", linewidth=1.5
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)
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ax3.axhline(y=0, color="gray", linestyle="-", linewidth=1, alpha=0.5)
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ax3.set_xlabel("Position (m)", fontsize=11)
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ax3.set_ylabel("Velocity (m/s)", fontsize=11)
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ax3.set_title("Vector Field & Phase Portrait", fontsize=12, fontweight="bold")
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ax3.grid(True, alpha=0.3)
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ax3.legend(fontsize=9)
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# Add colorbar
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cbar3 = plt.colorbar(scatter3, ax=ax3)
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cbar3.set_label("State", fontsize=10)
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cbar3.set_ticks([1.33, 1.67])
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cbar3.set_ticklabels(["Free Fall", "Spring-Damper"])
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# Plot 4: Energy
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ax4 = axes[1, 1]
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# Calculate energies
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KE = 0.5 * ball.m * y[:, 1] ** 2
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PE = ball.m * ball.g * y[:, 0]
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# Elastic potential energy when compressed
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elastic_PE = np.zeros_like(y[:, 0])
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for i, (pos, state) in enumerate(zip(y[:, 0], states)):
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if state == "spring_damper" and pos < ball.r:
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compression = ball.r - pos
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elastic_PE[i] = 0.5 * ball.k * compression**2
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total_E = KE + PE + elastic_PE
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ax4.plot(t, KE, label="Kinetic", linewidth=1.5, alpha=0.7)
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ax4.plot(t, PE, label="Gravitational PE", linewidth=1.5, alpha=0.7)
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ax4.plot(t, elastic_PE, label="Elastic PE", linewidth=1.5, alpha=0.7)
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ax4.plot(t, total_E, label="Total", linewidth=2, color="black", linestyle="--")
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# Mark transitions
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for t_trans in ball.transition_times:
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ax4.axvline(x=t_trans, color="green", linestyle=":", alpha=0.3, linewidth=1)
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ax4.set_xlabel("Time (s)", fontsize=11)
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ax4.set_ylabel("Energy (J)", fontsize=11)
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ax4.set_title("Energy Components", fontsize=12, fontweight="bold")
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ax4.grid(True, alpha=0.3)
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ax4.legend(fontsize=9)
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ax2.axhline(y=0, color="gray", linestyle="-", linewidth=1, alpha=0.5)
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ax2.set_xlabel("Position (m)", fontsize=11)
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ax2.set_ylabel("Velocity (m/s)", fontsize=11)
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ax2.set_title("Vector Field & Phase Portrait", fontsize=12, fontweight="bold")
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ax2.grid(True, alpha=0.3)
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ax2.legend(fontsize=9)
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plt.tight_layout()
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return fig
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@ -18,13 +18,21 @@
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[38
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Verify continuous control behavior across discrete mode transitions
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|
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}
|
||||
|
||||
\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}
|
||||
|
||||
\begin{frame}{Verified autonomous controllers can be created by building this
|
||||
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}
|
||||
|
||||
@ -0,0 +1,57 @@
|
||||
\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}
|
||||
@ -0,0 +1,73 @@
|
||||
\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}
|
||||
Loading…
x
Reference in New Issue
Block a user