in which, is an expression for the screw axis describing the ith joint axis in terms of the fixed frame with the robot in its zero position given above, and is the screw axis describing the ith joint axis, but after it undergoes the rigid body displacement instead of being at zero position. In other words, it is the Adjoint map of the screw axis for when the robot is no longer in zero position. Note that if is a transformation matrix where R is the rotation matrix and p is the position vector, then its adjoint representation can be calculated by: Note that the bracket notation [p] is the 3 × 3 skew-symmetric matrix representation of the position vector p. To learn more about the skewsymmetric matrix representation of a vector, you can refer to this lesson. The body Jacobian can then be calculated from the space Jacobian using the adjoint transformation (to learn more about the adjoint transformation in robotics, refer to this lesson): where is the inverse of the homogeneous matrix that was derived from forward kinematics earlier. 3 Summary Part 2 of the lesson series explored the theory behind screw theory-based numerical inverse kinematics for robotic manipulators, focusing on the Newton-Raphson iterative method. It also aimed to equip learners with the ability to calculate parameters and equations necessary for implementing a robot arm’s numerical inverse kinematics. In the next part, we will start working on implementing the vision-aided numerical inverse kinematics control of the robot arm. 11 Computer Vision News Vision-aided Screw Theory-based… Computer Vision News is very grateful to Madi and her team for another awesome lesson in robotics!
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