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  <title>Icarus Flight Simulations | Brandon Jacobson</title>
  <meta name="description" content="Project Icarus simulation work — from 1D PID altitude control to full 6-DoF quadrotor simulation with Kalman filter state estimation." />
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        <span>Icarus Simulations</span>
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      <!-- ── Page Hero ── -->
      <div class="project-page-hero">
        <h1 class="project-page-title">Project Icarus — Flight Simulations</h1>
        <p class="project-page-subtitle">
          Simulation work for Project Icarus, progressing from 1D PID altitude control
          to a full 6-DoF quadrotor simulation with Kalman filter state estimation and
          closed-loop trajectory tracking.
        </p>
        <div class="badge-row">
          <span class="badge">Python · NumPy · Matplotlib</span>
          <span class="badge">6-DoF Dynamics</span>
          <span class="badge">Kalman Filter</span>
          <span class="badge">PID Control</span>
        </div>
      </div>

      <!-- ════════════════════════════════════
           BLOCK 1 — Kalman Filter Update
           ════════════════════════════════════ -->
      <div class="sim-block" id="kf-simulation">
        <div class="sim-block-header">
          <h2 class="sim-block-title">6-DoF Simulation with Kalman Filter State Estimation</h2>
          <span class="sim-block-label">Latest</span>
        </div>

        <!-- Simulation GIF -->
        <div class="sim-gif-wrap">
          <img
            src="images/KF/drone_trajectory.gif"
            alt="6-DoF quadrotor simulation animating trajectory tracking through step waypoints"
            loading="eager"
          />
          <p class="sim-gif-caption">
            6-DoF quadrotor simulation — Kalman-filtered state estimates drive
            closed-loop PID control through a sequence of step waypoints.
          </p>
        </div>

        <!-- Key Highlights + Stack -->
        <div class="two-column" style="margin-bottom: var(--sp-8)">
          <div>
            <h3 style="font-size:0.95rem;font-weight:700;margin-bottom:var(--sp-3);color:var(--text)">Key Highlights</h3>
            <ul style="font-size:0.92rem;line-height:1.8;color:var(--text-muted)">
              <li>KF estimate converges to true position despite scattered GPS measurements.</li>
              <li>Closed-loop controller tracks step waypoints across X, Y, and Z simultaneously.</li>
              <li>Attitude remains stable through position transitions (&lt;30° max tilt).</li>
              <li>All four motor RPMs converge to steady-state hover after each waypoint.</li>
            </ul>
          </div>
          <div>
            <h3 style="font-size:0.95rem;font-weight:700;margin-bottom:var(--sp-3);color:var(--text)">Stack</h3>
            <ul style="font-size:0.92rem;line-height:1.8;color:var(--text-muted)">
              <li><strong>Language:</strong> Python, NumPy, Matplotlib</li>
              <li><strong>Dynamics:</strong> Nonlinear 6-DoF quadrotor model</li>
              <li><strong>Estimator:</strong> 6-state Kalman filter (position + velocity)</li>
              <li><strong>Attitude:</strong> Complementary filter on simulated IMU</li>
              <li><strong>Control:</strong> Cascade PID — position loop + attitude loop</li>
            </ul>
          </div>
        </div>

        <!-- Plots -->
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          <div class="plot-card">
            <div class="plot-card-img">
              <img
                src="images/KF/KF_Position_Estimation_Success_3_9_26.png"
                alt="Kalman filter position estimation: true position vs. KF estimate vs. noisy GPS across X, Y, and Z axes"
                loading="lazy"
              />
            </div>
            <div class="plot-card-caption">
              <strong>Kalman Filter — True vs. Estimated vs. GPS</strong>
              <p>
                KF estimate (red) tracks true position (blue) closely despite scattered GPS
                readings (green ×). Altimeter data (orange) fuses with GPS for Z-axis estimation.
              </p>
            </div>
          </div>

          <div class="plot-card">
            <div class="plot-card-img">
              <img
                src="images/KF/KF_Success_Position_Attitude_Motors_3_9_26.png"
                alt="Full system telemetry: position tracking, Euler attitude angles, and four motor RPMs over 30 seconds"
                loading="lazy"
              />
            </div>
            <div class="plot-card-caption">
              <strong>Full Telemetry — Position, Attitude &amp; Motors</strong>
              <p>
                X/Y/Z position tracks step waypoints (dashed) with clean transient response.
                Euler angles settle to near-zero in hover. All four motor RPMs converge
                after each commanded waypoint.
              </p>
            </div>
          </div>
        </div>
      </div>

      <!-- ════════════════════════════════════
           BLOCK 2 — 1D Simulation
           ════════════════════════════════════ -->
      <div class="sim-block" id="1d-simulation">
        <div class="sim-block-header">
          <h2 class="sim-block-title">1D Vertical Flight Simulation</h2>
          <span class="sim-block-label label-muted">Earlier Work</span>
        </div>

        <p style="font-size:0.95rem;color:var(--text-muted);line-height:1.8;margin-bottom:var(--sp-6)">
          The starting point for Icarus simulation — a 1D vertical flight model with PID altitude
          control, sensor noise, and low-pass filtering used to validate the control approach
          before extending to 6-DoF.
        </p>

        <div class="gallery" style="margin-bottom: var(--sp-8)">
          <figure class="media-card">
            <img src="images/Vertical_Thrust_Test1_Plot.png" alt="Baseline autonomous 10 m hover simulation plot" />
            <figcaption>Baseline autonomous 10&nbsp;m hover test — altitude and thrust vs. time.</figcaption>
          </figure>

          <figure class="media-card">
            <img src="images/NoisyTest1.png" alt="Noisy thrust response under PID control" />
            <img src="images/NoisyTest1_RPM.png" alt="Noisy RPM response under PID control" />
            <figcaption>Noisy thrust and RPM response under PID control during 10&nbsp;m hover.</figcaption>
          </figure>

          <figure class="media-card">
            <img src="images/LowPassTest1.png" alt="Low-pass filtered thrust signal" />
            <figcaption>Low-pass filtered thrust signal showing smoother control despite noise.</figcaption>
          </figure>
        </div>

        <div class="two-column">
          <div>
            <h3 style="font-size:0.95rem;font-weight:700;margin-bottom:var(--sp-3);color:var(--text)">Key Highlights</h3>
            <ul style="font-size:0.92rem;line-height:1.8;color:var(--text-muted)">
              <li>Modeled three-phase flight profile: ground → 10&nbsp;m hover → soft landing.</li>
              <li>Simulated noisy thrust and RPM measurements to evaluate controller robustness.</li>
              <li>Applied low-pass filtering to reduce thrust oscillations under sensor noise.</li>
            </ul>
          </div>
          <div>
            <h3 style="font-size:0.95rem;font-weight:700;margin-bottom:var(--sp-3);color:var(--text)">Stack</h3>
            <ul style="font-size:0.92rem;line-height:1.8;color:var(--text-muted)">
              <li><strong>Language:</strong> Python, NumPy, Matplotlib</li>
              <li><strong>Control:</strong> PID altitude control</li>
              <li><strong>Modeling:</strong> 1D thrust dynamics, noisy sensor measurements</li>
              <li><strong>Signal Processing:</strong> Low-pass filter on thrust commands</li>
            </ul>
          </div>
        </div>
      </div>

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