Improving the strategies employed to control robotic arms is of great importance because of the increase in their use in advanced supervisory control strategies, such as digital twins. The inverse kinematic (IK) control of manipulators requires an IK solution and an awareness of the singular configurations. This work presents a complete IK calculation system with singularity analysis for the UR5 robotic arm created by Universal Robots. For a specific robot pose, different angle solution sets are obtained, and one of these solution sets has to be selected to achieve movement continuity and avoid singularities. Two methods for this double purpose are proposed: one calculates all the solution possibilities, and the other obtains only one solution set by following a sequence of decisions and calculations clearly stated by a finite state machine (FSM). Both methods are effective in managing singularities. The FSM-based method complements the IK solution procedure with advantages in the number of computations and performance by producing results that would not lead the joints to move abruptly. The results prove that the presented methods select an IK solution that does not result in a singular configuration, and that most of the time, they lead to the same valid IK solution.
Inverse kinematic control of industrial robotic manipulators is extensively used, for this reason it is necessary to improve current direct and inverse kinematic solutions. While some previous solutions present partial sets of equations and others have some inconsistencies, this study presents the complete derivation of an alternative set of equations for the inverse kinematic solution for Universal Robots robotic arms, particularly the UR5. The herein inverse kinematic solution is obtained by applying the conventional Denavit-Hartenberg algebraic method and is validated with the direct kinematic solution.
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