Inverse Kinematics

1. General Derivation(起源)

• Not possible for serial Kinematics
• Must be derived(获得) with geometrical intuition
• Not always possible to find in closed-form
• Numerical solutions sometimes required

2. Non-Linear Porblem

• Example: TCP moves linearly along axis z
• Joints movements are highly non-linear

2.1 Non-unique solution

• Same TCP pose can be reached with different joints configurations
  • to solve this, we give singularities
• infinite joints solution exist for one single TCP pose to reduce
• Dependent linear value

3. Inverse Kinematics Steps

1. Decouple wrist from arm
   • find out that the position of the wrist point only depends on the first three joint axes of the robot
   • moving the fourth, fifth, sixth joint will not modify the position of the wrist point
   • so we can split into two part (wrist, arm) it called Decoupling

3. Base Frame and Tool

4. Adding a tool

5. Couple

• output of inverse kinematics is position of real joints

• They must be adjusted to calculate correct motor on target positions