![]() Simulation results show that implicit second-order methods give the best results. ![]() The application of implicit Euler, explicit trapezoid, implicit trapezoid and the weighted average method is considered, and an iteration is presented to calculate the implicit solutions. The accuracy of the closed-loop inverse kinematics algorithm is increased here by replacing the numerical integration with second-order and implicit numerical integration techniques. However, this can lead to unstable operation if the stability margin is reached. the convergence of the numerical solution to the real solution can be increased by increasing the value of a feedback gain parameter. The closed-loop inverse kinematics algorithm is a numerical approximation of the solution of the inverse kinematics problem, which is a central problem of robotics. The proposed method is demonstrated on the inverse positioning problem of an elbow manipulator and compared to the Damped Least Squares and the Levenberg-Marquardt methods, and it is shown that only the proposed method can leave the singular configuration in the singular direction. The conditions of regularizability are investigated, and bounds on the singular values of the regularized task Jacobian are given that can be used to create stable closed-loop inverse kinematics algorithms. A subproblem of the general inverse kinematics problem, the inverse positioning problem is considered for spatial manipulators consisting of revolute joints, and a regularization method is proposed that results in a regular task Jacobian in singular configurations as well, provided that the manipulator’s geometry makes movement in singular directions possible. the task Jacobian of the problem is singular. Inverse kinematics is a central problem in robotics, and its solution is burdened with kinematic singularities, i.e. The method is generalized to redundant orienting manipulators as well, and its application is demonstrated on two examples: a 3R Euler wrist and a 4R Hamilton wrist. It is shown that the Jacobian of generic manipulators composed of three rotational joints is always regularizable, so methods based on the Jacobian can be applied even in singular configurations. A regularization method is discussed that regularizes the Jacobian in singular configurations, by first transforming the angle-axis representation of angular velocities to infinitezimal rotation about an axis and infinitezimal translation perpendicular to that axis, then regularizing the infinitezimal translational motion in the new representation. In singular configurations, the differential inverse orientation problem can not be applied since the Jacobian becomes singular. These manipulators are composed of rotational joints, and thus inherently burdened with singularities. Orienting manipulators in robotics are used to achieve the desired orientation of the end effector of the manip-ulator.
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