2 Screw Theory-based Numerical Inverse Kinematics Using NewtonRaphson Iterative Method for Robotic Manipulators Inverse kinematics of robotic arms is the problem of finding joint variables that produce a desired end-effector configuration. Formally, the inverse kinematics problem can be stated as follows: Given an degree of freedom open chain, with forward kinematics represented by the variable homogeneous transformation , where are the joint variables, it is required to find a solution that satisfies , where is a desired (and given) homogeneous transformation and (IK: given , find such that ). Fig. 1 shows the difference between forward kinematics and inverse kinematics. Figure 1: Forward Kinematics vs. Inverse Kinematics in Robotics Inverse kinematics is a very important problem in the sense that here, we want to control the end-effector’s configuration for it to be able to interact with the world. However, it is a more complicated problem to solve than the forward kinematics. In forward kinematics, we will have a unique endeffector configuration for a given set of joint values, but the inverse kinematics problem can have zero, one, or multiple solutions for the joint values q that can produce the given desired end-effector configuration. There are two approaches to solving the inverse kinematics of an openchain robot: ➢ Analytic approach to inverse kinematics in which closed-form solutions for the joint variables can be found. Here, geometric approaches to the problem are utilized. These analytic solutions may not always exist. 7 Computer Vision News Vision-aided Screw Theory-based…
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