Robot Trajectory Optimization — 2-Link Planar Arm

A progressive 4-assignment project covering forward kinematics, trajectory generation, numerical optimization, and learning-based trajectory prediction for a 2-link planar robotic arm.

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Project Structure

robot-trajectory-optimization/
│
├── assignment1/
│   └── assignment1.md          # Forward Kinematics
│
├── assignment2/
│   └── assignment2.md          # Joint-Space Trajectory Generation
│
├── assignment3/
│   └── assignment3.md          # Trajectory Optimization in Joint Space
│
└── assignment4/
    ├── assignment4.md           # Learning-Based Trajectory Prediction
    ├── generate_dataset.py      # Dataset generation via optimization
    ├── train_model.py           # MLP training script
    └── app.py                   # Streamlit interactive dashboard

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Project Progression

Assignment	Topic	Key Concept
1	Forward Kinematics	Static pose computation
2	Trajectory Generation	Linear vs. polynomial interpolation
3	Trajectory Optimization	Numerical optimization (min acceleration)
4	Learning-Based Prediction	MLP trained on optimized trajectories

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Robot Model

A 2-link planar robotic arm with joint angles q1, q2 and link lengths l1, l2.

Forward Kinematics:

x = l1·cos(q1) + l2·cos(q1 + q2)
y = l1·sin(q1) + l2·sin(q1 + q2)

Workspace:

• Maximum reach: R_max = l1 + l2
• Minimum reach: R_min = |l1 - l2|

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Dependencies

pip install numpy scipy matplotlib torch scikit-learn streamlit

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How to Run

Assignment 3 — Trajectory Optimization:

python assignment3/trajectory_optimization.py

Assignment 4 — Generate Dataset:

python assignment4/generate_dataset.py

Assignment 4 — Train Model:

python assignment4/train_model.py

Assignment 4 — Launch Dashboard:

streamlit run assignment4/app.py

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Key Results

• Optimized trajectories achieve significantly lower acceleration cost than polynomial trajectories
• The trained MLP approximates optimized trajectories with near-instant inference
• The interactive dashboard enables real-time comparison of optimized vs. learned trajectories in both joint space and Cartesian space