ENPM662_final

This project contains code and outputs for the ENPM662 final, including DH forward kinematics derivations, numeric validation, and an IK camera-tracking simulation with visualizations.

Using uv

1. Install uv (choose one)

brew install uv
# or
pipx install uv

2. Create/sync the environment

uv sync

3. Run

# Symbolic FK derivation + LaTeX output
uv run python src/q1_3.py

# DH vs geometric composition validation
uv run python src/q1_4.py

# IK camera-tracking simulation + plots
uv run python src/q1_sim.py

Project structure

• src/q1_3.py: builds DH parameters with Sympy, computes A1~A6, T0_6, T0_EE, and prints LaTeX.
• src/q1_4.py: computes FK via DH and via geometric composition, then validates them numerically.
• src/q1_sim.py: IK solver, camera tracking path generation, error metrics, and visualization outputs.
• outputs/fig_layout_actor_path.png: XY layout of actor and camera paths.
• outputs/fig_joint_trajectories.png: joint trajectories for d0 and q2~q6 over time.
• outputs/fig_camera_path_with_arrows.png: 3D camera path with optical axis arrows.

Implementation overview

1) DH Forward Kinematics (src/q1_3.py)

• Use the standard DH form A = Rz(theta) * Tz(d) * Tx(a) * Rx(alpha).
• Build A1~A6 from the given DH table.
• Add the fixed camera offset T6_EE = Tx(Lc) * Ty(-hc) to obtain T0_EE.
• Print all intermediate matrices and LaTeX strings for reporting.

2) DH vs Geometric Composition Validation (src/q1_4.py)

• Multiply the DH chain to get T_dh.
• Build T_geo from the equivalent geometric sequence of transforms.
• Compare numeric test cases to confirm FK consistency and rotation orthonormality.

3) Camera-Tracking IK Simulation (src/q1_sim.py)

• Generate the actor's staircase arc path, then derive desired camera positions and view directions along the path.
• IK is solved in two stages:
  • Position IK: damped least-squares to reach the desired camera position.
  • Pointing IK: refine with optical-axis direction error.
• Solve joints at each timestep, then wrap/unwrap angles for continuity.
• Generate path and joint trajectory plots, and print summary error metrics.