Inverse Kinematics

Inverse Kinematics

• The opposite problem of forward kinematics

The Workspace of the Robot

• The workspace of the robot is where its end effector can reach.

Example of Workspace for 2-Link Planar Robot

• it's workspace is shaped like a doughnut.

• Case 1: Anything outside the outer boundary is unreachable. 0 solution

• Case 2: Exactly on the outer boundary, there is only one solution.

• Case 3: On its workspace (between inner and outer boundary), it has 2 solutions.

• Case 4: Exactly on the inner boundary, there is one solution.

• Case 5: Anything inside the inner boundary is unreachable. 0 solution.

Inverse Kinematics + Orientation. Is it possible??

• Answer: Forget it. it's not possible. solution for 3 variables (a, b, gamma) with only joints (q1 and q2) doesn't exist. There isn't enough DOF.

• So, add one more Joint q3 and it becomes possible now.

Extending our intuition from 2D to 3D

• 3 variables (x, y, theta) vs 6 variables (x, y, z, roll, pitch, yaw)

The Human Arm

• 7 degrees of freedom

• 3 DOF at the shoulder, 1 DOF at the elbow and 3 DOF at the wrist.

• 7 DOF is actually redundant for a 3D manipulator.

Degrees of Freedom in Robots

• A robot with 7 DOF is more expensive than a 6 DOF robot.

• 7 DOF is when you might have obstacles in the environment in the robot workspace.

• Most robot arms stop at 7 DOF.