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Achieving extreme precisions for multiple manipulators using a proper coupled neural network matrix method and LabVIEW instrumentation

In controlling the movements of the end-effector and joints of a manipulator in the workspace, an important problem is to identify the joints' best relative displacements to assure extreme precisions for the end-effector movements. Applications where multiple manipulators with a common controller are to be controlled in 3D space are more challenging compared to single robot control since the movements of the end-effectors of all robots must be determined using complex forward and inverse kinematics. In this paper, to solve the inverse kinematics problem in robots with redundant chains, a hybrid method that combines the convergence process through proper Iterative Pseudo Inverse Jacobian Matrix Method (IPIJMM) with the filtering of the errors by the Bipolar Sigmoid Hyperbolic Tangent Neural Network Method with Time Delay and Recurrent Links (BSHTNNM-TDRL). We have presentpd mathematical models of forward kinematics of a system of multiple manipulators, as well as the developed proper iterative algorithm to obtain spatial conventional and unconventional curves in different Euler planes for a case study of three robots moving simultaneously with extreme end-effector precision of less than 0.001 mm. We have shown how a system of three robots can be considered as a single parallel robot structure with three independent robotic components. The presented method is a numerical iterative approximation technique equipped with an intelligent error reduction algorithm, and together with the employed Virtual Instrumentations (VI) can be generalized to other robots tracking any conventional and unconventional space curves.