Inverse Kinematics for Robotics using Neural Networks.

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Inverse Kinematics for Robotics using Neural
Networks.
Authors Sreenivas Tejomurtula., Subhash Kak.
1998
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Sub-Topics

• Robotics.
• Inverse Kinematics.
• Neural Networks.

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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.

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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)).

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

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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.

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Forward map for 2 planar arm
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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.

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• 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.

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Neural Network architecture
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• 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.

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

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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.

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