Review: Neural Network Control of

Robot Manipulators;

Frank L. Lewis;

1996

Sub-topics Control Theory/ System Theory.

Closed loop controllers.

Adaptive Control.

PID

Neural Networks.

Dynamics in Robotics.

Control Theory Systems that use feed-back loops to regulate a

control parameter about a set value.

For example: The core temperature of the human

body must be regulated about a set value, and there

are biological sensors and actuators that allow this.

Also consider how you adjust the tap in the shower

to regulate the temperature of the water to a

comfortable temperature. Also: Notice how your

most comfortable temperature normally rises during

your shower and you adjust the tap accordingly.

Below: Adaptive control is important where tuning

parameters are uncertain.

Proportion + Integration + Differentiation.

Closed loop system to maintain a small error e

between the set value and the actual value for

the control parameter.

The parameters Kv, Ki, Kd are tuned for the

particular task as they represent the strength

of the effectors .

PID

Neural Networks in Control Theory Rejected.

Why? - The author claims previous attempts to introduce

Neural Networks into Control Theory have lacked

theoretical proofs and repeatable design algorithms.

The challenges: providing repeatable design algorithms;

online learning algorithms (no offline tuning);

demonstrating closed loop trajectory following, computing

various weight tuning gradients and demonstrate the

weights remained bounded given unmodelled dynamics.

Interested in NN because of function approximation

property – which fails to hold for adaptive control.

Neural Network Architecture

3 layered architecture.

Model free.

Continuous Differentiable activation function .

Equation 1 shows f(x) the true function and

Equation 2 shows approximation, ^f(x).

Dynamics in Robotics Once we know the target position of the end effectors

(having used inverse kinematics), dynamics deals with

what forces are required to perform that action, ie; of

moving the joints along a trajectory.

The matrices : M is the inertia, V is the

centripetal/coriolis, G is the gravity and F is the friction,

whilst is the input torque and d represents bounded

unknown disturbances.

Calculating the trajectory.The joint force vector is q Rn for n joints.

Quantities are imperfectly known and difficult to

determine

Robotic Controller Structure How about try to estimate unknown information

using adaptive control?

We have ˜f is the tracking error which is found

using adaptive control and v(t) is the robustifying

signal to compensate for unstructured/ un-modelled

dynamics.

Use NN instead of Adaptive Control

Parameter Tuning Not just neural network weights need to be “tuned”.

Tuned by backpropagation as in Table and using

12.

NN controller proven to track trajectory.

Trajectory error bounded.

Outer loop is a PD controller and Kv represents the PD

gains.

Neural Network weights are initialised to zero.

The larger the NN, the smaller the PD gains. Removal of

the NN causes the system to become a PD Controller.

But errors due to parameter-uncertainty will be high too.

The more nodes in the network, the more difficult to

implement because each node needs an 'integrator'.

Option to incorporate a partitioned Neural Networks to

enhance controller structure and to increase the speed

of the weight tuning algorithm.

Comparison of Adaptive Control and

NN, given un-modelled dynamics

Neural Network Controller.

Left: Ideal Conditions; Right Adaptive Controller

Hebbian Tuning

Hebbian tuning provides very good closed loop

performance. Works well because of ^V update and

e modification second terms.

Application: Force and position controllers

Grinding, Milling and Surface Finishing.