Pick_and_Place_Eigenvalues_Presentation.pptx

ROOBOOT

1. Eigenvalues & Eigenvectors in Pick-and-Place Robot Understanding Motion Stability and Control in a 2-Link Robot Using MATLAB

2. Problem Statement • Simulate a 2-link pick-and-place robotic arm. • Use eigenvalues & eigenvectors to analyze motion. • Ensure smooth and stable movement from initial to target position.

3. 2-Link Pick-and-Place Robot Model • Link 1 (L1) and Link 2 (L2) connected by revolute joints. • Moves from an initial position to a target position. • End-effector follows a smooth trajectory.

4. Role of Eigenvalues & Eigenvectors • Eigenvalues indicate stability: - Negative values: Stable motion. - Positive values: Unstable motion. • Eigenvectors represent principal movement directions. • Helps in analyzing dynamic response of the robot.

5. MATLAB Implementation • Define robot parameters (L1, L2, joint angles). • Compute Jacobian matrix J at each step. • Calculate eigenvalues and eigenvectors of J. • Visualize eigenvectors as arrows at the end-effector.

6. Results & Animation • Robot moves smoothly from initial to target position. • Eigenvalues change dynamically, indicating motion stability. • Eigenvectors help visualize the principal motion directions.

7. Conclusion • Eigenvalues & eigenvectors are key to motion stability. • Helps in trajectory planning and smooth operation. • Important for advanced robotics and automation.