空间代数与运动学

操作的数学基础：空间代数、旋转表示（欧拉角、四元数、旋转矩阵）、齐次变换、正运动学（DH 参数）、逆运动学和雅可比矩阵。

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