\section{Schedule, Milestones, and Deliverables}

\textbf{Heilmeier Question: How long will it take?}

The complete research plan is now established. Section 6 demonstrated that this work addresses a \$21--28 billion annual cost barrier and establishes a generalizable framework for safety-critical autonomous systems. The final Heilmeier question addresses timing and feasibility within a doctoral timeline.

This research will be conducted over six trimesters (24 months) of full-time effort following the proposal defense in Spring 2026. The University of Pittsburgh Cyber Energy Center and NRC Fellowship provide all computational and experimental resources. The work progresses sequentially through three main research thrusts, culminating in integrated demonstration and validation.

The first semester (Spring 2026) focuses on Thrust 1, translating startup
procedures into formal temporal logic specifications using FRET. This
establishes the foundation for automated synthesis by converting natural
language procedures into machine-readable requirements. The second semester
(Summer 2026) addresses Thrust 2, using Strix to synthesize the discrete
automaton that defines mode-switching behavior. With the discrete structure
established, the third semester (Fall 2026) develops the continuous controllers
for each operational mode through Thrust 3, employing reachability analysis and
barrier certificates to verify that each mode satisfies its transition
requirements. Integration and validation occupy the remaining three semesters. 

Figure \ref{fig:gantt} shows the complete project schedule including research thrusts, major milestones, and planned publications.

\begin{figure}[htbp]
    \centering
    \begin{ganttchart}[
        hgrid,
        vgrid={*{4}{draw=none}, dotted},
        x unit=0.4cm,
        y unit title=0.6cm,
        y unit chart=0.4cm,
        title/.append style={fill=gray!30},
        title height=1,
        bar/.append style={fill=blue!50},
        bar height=0.5,
        bar label font=\small,
        milestone/.append style={fill=red, shape=diamond},
        milestone height=0.5
    ]{1}{24}
    
    % Timeline headers
    \gantttitle{2026}{12}
    \gantttitle{2027}{12} \\
    \gantttitle{Spring}{4}
    \gantttitle{Summer}{4}
    \gantttitle{Fall}{4}
    \gantttitle{Spring}{4}
    \gantttitle{Summer}{4}
    \gantttitle{Fall}{4} \\
    
    % Major thrusts
    \ganttbar{Thrust 1: Procedure Translation}{1}{5} \\
    \ganttbar{Thrust 2: Discrete Synthesis}{4}{10} \\
    \ganttbar{Thrust 3: Continuous Control}{9}{15} \\
    \ganttbar{Integration \& Simulation (TRL 4)}{13}{17} \\
    \ganttbar{Hardware-in-Loop Testing (TRL 5)}{16}{21} \\
    \ganttbar{Dissertation Writing}{18}{24} \\[grid]
    
    % Milestones row
    \ganttbar[bar/.append style={fill=orange!50}]{Milestones}{1}{24}
    \ganttmilestone{}{4}
    \ganttmilestone{}{8}
    \ganttmilestone{}{12}
    \ganttmilestone{}{16}
    \ganttmilestone{}{20}
    \ganttmilestone{}{24} \\
    
    % Publications row
    \ganttbar[bar/.append style={fill=green!50}]{Publications}{1}{24}
    \ganttmilestone{}{8}
    \ganttmilestone{}{16}
    \ganttmilestone{}{20}
    
    \end{ganttchart}
    \caption{Project schedule showing major research thrusts, milestones (orange row), and publications (green row). Red diamonds indicate completion points. Overlapping bars indicate parallel work where appropriate.}
    \label{fig:gantt}
\end{figure}

\subsection{Milestones and Deliverables}

Six major milestones mark critical validation points throughout the research:

\textbf{M1 (Month 4):} Confirms that startup procedures have been successfully translated to temporal logic using FRET with realizability analysis demonstrating consistent and complete specifications.

\textbf{M2 (Month 8):} Validates computational tractability by demonstrating that Strix can synthesize a complete discrete automaton from the formalized specifications. Delivers a conference paper submission to NPIC\&HMIT documenting the procedure-to-specification translation methodology.

\textbf{M3 (Month 12):} Achieves TRL 3 by proving that continuous controllers can be designed and verified to satisfy discrete transition requirements. Delivers an internal technical report demonstrating component-level verification.

\textbf{M4 (Month 16):} Achieves TRL 4 through integrated simulation demonstrating that component-level correctness composes to system-level correctness. Delivers a journal paper submission to IEEE Transactions on Automatic Control presenting the complete hybrid synthesis methodology.

\textbf{M5 (Month 20):} Achieves TRL 5 by demonstrating practical implementability on industrial hardware. Delivers a conference paper submission to NPIC\&HMIT or CDC documenting hardware implementation and experimental validation.

\textbf{M6 (Month 24):} Completes the dissertation documenting the entire methodology, experimental results, and research contributions. 
