ENPM667 Project 2 – Double-Pendulum Crane Control

This repository contains the source code, scripts, and figures used to solve ENPM667 Project 2. The project studies a double-pendulum gantry crane model and walks through controllability, LQR design, observability, Luenberger observer synthesis, and LQG output feedback on both the linearized and nonlinear dynamics.

Environment setup

Requirements

• Python 3.11 (per pyproject.toml)
• uv 0.4+ or plain pip/venv
• OS X / Linux with BLAS/LAPACK available (for SciPy) and a working LaTeX-free Matplotlib backend

Quick start with uv (recommended)

uv venv                       # creates .venv tied to Python 3.11
source .venv/bin/activate     # or .venv\\Scripts\\activate on Windows
uv sync                       # installs runtime deps from pyproject.toml / uv.lock

uv sync honors the locked versions found in uv.lock. Re-run it whenever dependencies change.

Daily uv workflow

• Run scripts through the managed env without activating manually:

  uv run python src/component1_C.py
  uv run python src/component1_D.py

• Add extra packages (dev or runtime) and update pyproject.toml/uv.lock in one shot:

  uv add black ruff
  uv add --dev pytest

• Upgrade existing dependencies as needed:

  uv lock --upgrade sympy
  uv sync

Alternative: vanilla pip

python3.11 -m venv .venv
source .venv/bin/activate
python -m pip install --upgrade pip
pip install "matplotlib<3.9" "numpy<2" "pandas>=2.3.3" \
            "roboticstoolbox-python>=1.1.1" "scipy<1.13" \
            "spatialmath-python>=1.1.15" "sympy>=1.14.0"

Developer tooling (optional):

pip install "black>=25.9.0" "ruff>=0.13.2" "pytest>=8.4.2"

Running the components

All scripts assume the environment above is active and are invoked from the project root.

Component 1 – C) Controllability

python src/component1_C.py

Outputs the symbolic controllability matrix, its rank, determinant, and an optional numeric rank check. Edit the subs_example dictionary to try alternate physical parameters.

Component 1 – D) LQR search and simulations

python src/component1_D.py

• Sweeps candidate diagonal Q and scalar R, computes LQR gains, and simulates both the linearized model (A - B K) and the nonlinear crane dynamics.
• Saves a comparison table (component1_D_comparison_table.png) plus best-design state/control plots (component1_D_best_{x,theta1,theta2,u}.png). Copies of these artifacts live under fig/component1_D/.
• Adjust the Q_candidates, R_candidates, initial condition x0, or time span t_span to explore different cases.

Component 2 – E) Observability checks

python src/component2_E_observability.py

Runs the dual controllability test for four output selections, prints symbolic ranks, and repeats the test numerically for the project’s nominal parameters. Modify C_list to try new sensor groupings.

Component 2 – F) Luenberger observers

python src/component2_F_observer_design.py

• Reuses Design #2’s LQR gain, builds observers for each observable output option, and places poles using scipy.signal.place_poles.
• Simulates the coupled plant-observer system for both the linearized and nonlinear models, reporting integral squared error, peak estimation errors, and control magnitudes.
• Saves a CSV-like table image (component2_F_observer_comparison_table.png) and best-case time-series figures (component2_F_case{n}_{lin,nonlin}.png). Curated copies are stored under fig/component2_F/.
• Tweak speed_factors, the initial states x0, or simulation length t_final to examine different observer aggressiveness levels.

Component 2 – G) LQG controller

python src/component2_G_LQG.py

Constructs an LQG controller (Design #2 LQR + continuous-time Kalman filter for y = (x, θ1, θ2)), injects process/measurement noise, and simulates both the linearized and nonlinear plants via RK4 integration. Generates four figures showing state estimates and control effort:

• component2_G_LQG_y_xth1th2_linear_true_vs_hat.png
• component2_G_LQG_y_xth1th2_linear_states.png
• component2_G_LQG_y_xth1th2_nonlinear_true_vs_hat.png
• component2_G_LQG_y_xth1th2_nonlinear_states.png

Copies of the figures intended for the report live under fig/component2_G/. Adjust noise levels (sigma_w, sigma_x_m, sigma_th1_deg, sigma_th2_deg), actuator saturation (U_MAX), or seeds to study robustness.

Tips for extending or grading

• Each script is self-contained; no package install is required beyond dependencies listed in pyproject.toml.
• Numerical experiments that produce PNGs write to the project root. Move them into the appropriate fig/ subfolder before committing, or update the scripts’ plt.savefig paths if you want them to land there directly.
• There is no automated test suite. To verify results, re-run the scripts after making parameter/code changes and inspect the console outputs and regenerated figures.
• Use ruff and black from the optional dev dependencies to keep code formatting consistent when modifying the scripts.

License

The project is distributed under the Apache License 2.0. Refer to that file for details on reuse and attribution.