This paper presents a novel real-time robust inverse kinematics (IK) algorithm for robot manipulators using a modified Newton Raphson (MNR) method. The modification of the conventional NR algorithm refers to the modified Jacobian matrix, which specifically excludes the Euler angles and instead incorporates information regarding the alignment of each end-effector’s attached frame with the global frame. This enables directly controlling each end-effectors frame in the global frame, while ensuring precise configuration accuracy. Additionally, a weighted least-norm method with a clamping concept is presented to enhance hardware safety and reliability. This guarantees that the joints remain within defined limitations but may significantly sacrifice the main task accuracy. Subsequently, the algorithm performs task prioritization with a priority matrix, which intends to restore partial accuracy of the main task by prioritizing either the desired position or orientation. To ensure smooth switching between tasks as the joint reaches its maximum limit, a damped extension of the clamping velocity is employed to gradually deactivate the lower-priority task. Simulation and experimental results on a six-DOF robot manipulator, with mean calculation times of 32 . 8 μ s , and 105 μ s , respectively validate the proposed method’s real-time capability and accuracy (position error ≈ 4 . 5 e − 3 mm , orientation error ≈ 1 e − 5 ∘ ). Moreover, the proposed IK generates smooth joint trajectories, prevents joint limitations, and restores partial accuracy when joint reaches their limits.
Khan et al. (Sun,) studied this question.