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Use the MATLAB Adaptive Neuro-Fuzzy Inference System (ANFIS) to learn the Inverse Kinematics of a planar 2R manipulator. Training data should be generated using the Forward Kinematics functions over the full range of motion of the joints (specification of the arm geometry will be given in a separate document (last page)).
a. You will need to use separate ANFIS networks for each joint of the manipulator and should aim to achieve accurate positioning over the full range of motion by adjusting the design of the ANFIS networks and training/validation data.
b. Learning performance should be monitored using appropriate validation to ensure avoidance of under or over-fitting.
c. After training, further testing should be used to compare solutions for accuracy in position (but not orientation) of the end effector over the full reachable workspace.
2. Repeat task 1 using a single feedforward multilayer network instead of ANFIS networks.
a. Experiment with different training and validation methods to achieve good accuracy without excessively long training time.
3. Evaluate the results of the networks in tasks 1 and 2 using a common test set uniformly sampled from the full reachable workspace of the manipulator end-effector.
4. Add another link to the arm to make a 3R planar manipulator and repeat tasks 1, 2 and 3. Again, the task is only concerned with end effector position. How does the accuracy of the 3R manipulator compare with the 2R?
5. From material delivered in the module and your own independent research, find reasons for the poor performance of the direct inverse approach used in task 4. Suggest other approaches which may be used to achieve higher accuracy and include discussion of their advantages and disadvantages with full citation of your research sources. Note that you are not required to implement these approaches.
All experiments are to be carried out using MATLAB and the Fuzzy Logic and Deep Learning Toolboxes. Full code listings are to be included as an appendix to the report (this is not included in the word count).