1. Inverse Kinematics for Robotics using Neural Networks. Authors: Sreenivas Tejomurtula., Subhash Kak. 1998

2. Sub-Topics Robotics. Inverse Kinematics. Neural Networks.

3. Robotics Autonomous physical agents. Sensors – observing the environment. Actuators – changing the environment. Typical in manufacturing industry. Efficient at performing precise, simple repetitive tasks, eg welding, spray painting. Some tasks are too dangerous for humans.

4. Inverse Kinematics The structure of a robotic manipulator consists of a chain of rigid limbs connected by joints. The end effector is the last part of the chain and makes physical contact with the environment. Kinematics works out the end effector position(s) (x,y,z) as a function of the joint angles  Inverse Kinematics is the opposite: = f((x,y,z)).

5. Inverse Kinematics says “take our goal position and find how to get there” - (what angles are required).

7. How to solve IK? Analytical solutions.  Fast.  Design based – determines robot design.  Poor generalisation.  Handles singularities well. Numerical methods.  Slow  Good generalisation to arbitrary robot design.  Handles singularities poorly.

8. Forward map for 2 planar arm

9. Neural Networks (A new alternative) Train the neural network to learn the forward mapping (typically). “Invert” the neural network to find the input angles of the forward mapping. 3 existing methods applied to IK:  Optimization: Approximate a non-linear function between layers and solve using non-linear programming.

10.  Iterative: Given we know the desired output lets find the best input-output mapping to match the output by searching a path in input space.  Error back-propagation: Plug in the desired output into the forward mapping network. Use back- propagation to propagate the error back to the input units and so the input steps along input space and let the weights revert back to their original settings each iteration.

11. Neural Network architecture

12. Forward kinematics can be determined for most manipulators except for those with redundant joints. Good initial guess for input is made using “Corner Classification”. Since architecture is based on equations no training is required!! IE, weights are taken from equations. Some of the weights are non-linear which makes error back-propagation tricky. Eg, for sin and cos weights we make a decision at the neighbourhood to determine a sign change.

13. Once we have convergence we test to see whether joint angles are within their allowable range.

16. Conclusion Useful in real-time applications as it generates many accurate solutions quickly. Alternatively, Kohonen maps require a long optimization process. Although there are revolute, prismatic, helical, cylindrical, spherical and planar joints, only revolute and prismatic joints are regarded here. Also it does not handle redundant joints. Unlike numerical techniques, the computational requirement is not based on the number of joints but the network architecture.

17. Must generate good initial guesses for the input. NN design introduces more structure, not less.