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inverse kinematics

Determining what joint angles are needed to position the end-effector at a specific target location. Think: “I want my hand at this point in space—what angles do I need?”

The opposite of forward kinematics.


What it is:

The mathematical process of calculating what angles each joint needs to be at so that the robot's hand (end-effector) reaches a desired position and orientation in space.

The inverse problem:
  1. Forward kinematics — You know all the joint angles → calculate where the hand is
  2. Inverse kinematics — You know where you want the hand to be → calculate what angles achieve that
Why it's essential:

When you command a robot "move your gripper to position X, Y, Z in space," the robot doesn't work in those coordinates natively—it works by rotating individual joints. Inverse kinematics is the translation layer that converts your high-level spatial goal into specific joint commands.

The challenge:
  1. There may be multiple solutions (different joint configurations that reach the same point)
  2. There may be no solution (the target is physically unreachable)
  3. The math can be computationally expensive to solve in real-time
Practical example:

You want to pick up a cup on a table. You specify the cup's location (X, Y, Z coordinates). The inverse kinematics algorithm instantly calculates: "Rotate shoulder to 45°, elbow to 90°, wrist to 120°" to get your gripper exactly where it needs to be.

Connection to other concepts:

The Jacobian matrix is the mathematical foundation that makes inverse kinematics calculations possible—it provides the geometric relationships needed to solve the problem.













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