Inverse Kinematics for Robotics
using Neural Networks.
Authors: Sreenivas Tejomurtula., Subhash Kak.
Autonomous physical agents.
observing the environment.
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.
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
Inverse Kinematics is the opposite:
Inverse Kinematics says “take our goal position
and find how to get there”
(what angles are
How to solve IK?
determines robot design.
Handles singularities well.
Good generalisation to arbitrary robot design.
Handles singularities poorly.
Forward map for 2 planar arm
Neural Networks (A new alternative)
Train the neural network to learn the forward
“Invert” the neural network to find the input
angles of the forward mapping.
3 existing methods applied to IK:
Optimization: Approximate a non
between layers and solve using non
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.
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
Neural Network architecture
Forward kinematics can be determined for most
manipulators except for those with redundant joints.
Good initial guess for input is made using “Corner
Since architecture is based on equations
training is required
!! IE, weights are taken from
Some of the weights are non
linear which makes
propagation tricky. Eg, for sin and cos
weights we make a decision at the neighbourhood
to determine a sign change.
Once we have convergence we test to see
whether joint angles are within their allowable
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.
Must generate good initial guesses for the input.
NN design introduces more structure, not less.