Learning multiple solution branches for the direct kinematics of parallel manipulators

It is well known that, the direct kinematics of parallel manipulators requires solving highly non-linear equations and it has non-unique multiple sets of solutions referred to the assembly modes. This complexity inhibits the real-time applications of such manipulators, so the Kohonen´s self-organizing map (SOM) is proposed in this paper to classify and learn the multiple solution branches of the direct kinematics and then provide a unique real-time solution in among the assembly modes based on a certain class code. Due to not only the classifïcation but also the associative memory learning abilities of the SOM, a passive joint angle variables vector, the output end-effector pose vector and a class code are associated with the active joint angle variables vector as an input vector to the SOM in the off-line learning phase. In the on-line testing phase, only the active joint angle variables vector and the class code, as a subspace of the input vector, are fed to the SOM to obtain the end-effector pose vector. In order to further fine timing the SOM output, the Jacobian matrix calculated at the output layer is used to obtain an accurate end-effector pose vector. Simulations are conducted for 3-RRR planar parallel manipulator to evaluate the performance of the proposed method. The results proved high accuracy of the desired unique solution in real-time.