Spatial Algebra & Kinematics¶

Mathematical foundations for manipulation: spatial algebra, rotation representations (Euler angles, quaternions, rotation matrices), homogeneous transforms, forward kinematics (DH parameters), inverse kinematics, and Jacobian matrices.

Learning Objectives¶

1. Spatial Algebra Foundations¶

1.1 Position & Orientation¶

1.2 Rotation Representations¶

1.3 Homogeneous Transformation Matrices¶

2. Forward Kinematics¶

2.1 DH Parameters¶

2.2 Kinematic Chain¶

2.3 FK with Python (roboticstoolbox)¶

3. Inverse Kinematics¶

3.1 Analytical IK¶

3.2 Numerical IK (Newton-Raphson, Levenberg-Marquardt)¶

3.3 IK with Robotics Toolbox¶

4. Jacobian Matrices¶

4.1 Geometric Jacobian¶

4.2 Analytical Jacobian¶

4.3 Singularities¶

5. Differential Kinematics¶

5.1 Velocity Kinematics¶

5.2 Jacobian Pseudo-Inverse¶

5.3 Redundancy Resolution¶

6. Practice: FK/IK for a 6-DOF Arm¶

Exercises¶

References¶