take the end-effector frame {b} to the desired frame {d}. To learn about reference frame assignment in robotics and the homogeneous transformation matrices to represent pose in robotics, you refer to the orientation in robotics and pose in robotics lessons. To have a brief review of the Newton-Raphson method for nonlinear root finding, you can refer to this lesson. To find the numerical screw theory-based inverse kinematics of open-chain manipulators, follow the following algorithm: 1. Initialization: Given (transformation of the desired frame with respect to space frame) and an initial guess of joint variables , set 2. Set . While the algorithm is not converged: ➢ Set ➢ Increment Where is the current joint angles guess, is the body twist calculated from the error between the current end-effector configuration and the desired configuration, and is the pseudoinverse of the body Jacobian matrix evaluated at the current joint angles . To learn about how to calculate the forward kinematics of robot manipulators, refer to this lesson, for Twists refer to this lesson, and to learn about screw theory based Jacobian matrix calculation, refer to this lesson. Figure 3: Robot arm depicted in home position with screw axes and link 9 Computer Vision News Vision-aided Screw Theory-based…
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