a1 Department of Production Engineering and Mechanical Design, Faculty of Engineering, Tanta University, Tanta, Egypt
Contrary to the inverse kinematics, the forward kinematics of parallel manipulators involves solving highly non-linear equations and provides more than one feasible end-effector pose, which are called the assembly modes, for a given set of link lengths or joint angles. Out of the multiple feasible solutions, only one solution can be achieved from a certain initial configuration. Therefore, in this paper, the Kohonen's self-organizing map (SOM) is proposed to learn and classify the multiple solution branches of the forward kinematics and then provide a unique real-time solution among the assembly modes. Each solution of the multiple feasible ones is coded using IF-THEN rules based on the values of the passive joint variables. Due to not only the classification but also the associative memory learning abilities of the SOM, the passive joint variables vector, the end-effector pose vector, and this class code are associated with the active joint variables vector constituting the input vector to the SOM in the offline learning phase. In the online testing phase, only the active joint variables vector and the class code are fed to the SOM to obtain the unique end-effector pose vector. The Jacobian matrix calculated at the SOM output layer is used for further fine tuning this output to obtain an accurate end-effector pose vector. Simulations are conducted for 3-RPR and 3-RRR planar parallel manipulators to evaluate the performance of the proposed method. The results proved high accuracy of the desired unique solution in real-time.
(Accepted October 06 2011)
(Online publication November 14 2011)