Computer Vision News 8 ➢ Iterative numerical approach to inverse kinematics in which Jacobian is used to iteratively find a solution using the Newton-Raphson method. An initial guess for the solution should be made, and then this method iteratively pushes the initial guess towards a solution. This approach will only give us one solution and not all possible solutions. If the inverse kinematics equations cannot be solved analytically, iterative numerical techniques may be utilized. Moreover, numerical methods are frequently employed to enhance the precision of analytic solutions, even when such solutions are available. In this case, the analytic solution can be used as an initial guess for the iterative numerical approach. For this purpose, we will use Newton–Raphson method, which is an integral method in nonlinear root finding. In situations where there is no exact solution exists, we will need optimization methods to find the closest approximate solution. If the manipulator is redundant, there will be infinite solutions to the inverse kinematics problem. In this case, we need to find a solution that is optimal with respect to some criterion. Now, let’s start by providing a general algorithm for numerical inverse kinematics using the Newton-Raphson method. Suppose that is the pose of the end-effector frame {b} in the base frame {s} (calculated from the forward kinematics) and the desired end-effector configuration is given by the transformation matrix as depicted in Fig. 2 below. Solving the inverse kinematics means that we need to find the set of joint angles that can Lessons in Robotics Figure 2: llustration of the pose of the end-effector frame in the base frame, , and the desired end-effector configuration is given by the transformation matrix . Solving the inverse kinematics means that we need to find the set of joint angles that can take the end-effector frame {b} to the desired frame {d}.
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