# A QP Artificial Neural Network inverse kinematic solution for accurate robot path control

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## Abstract

In recent decades, Artificial Neural Networks (ANNs) have become the focus of considerable attention in many disciplines, including robot control, where they can be used to solve nonlinear control problems. One of these ANNs applications is that of the inverse kinematic problem, which is important in robot path planning. In this paper, a neural network is employed to analyse of inverse kinematics of PUMA 560 type robot. The neural network is designed to find exact kinematics of the robot. The neural network is a feedforward neural network (FNN). The FNN is trained with different types of learning algorithm for designing exact inverse model of the robot. The Unimation PUMA 560 is a robot with six degrees of freedom and rotational joints. Inverse neural network model of the robot is trained with different learning algorithms for finding exact model of the robot. From the simulation results, the proposed neural network has superior performance for modelling complex robot’s kinematics.

## Key Words

Artificial Neural Network Robot Path Control PUMA Robot## Nomenclature

*a*_{i}The distance from

*Z*_{i}to*Z*_{ i+1}measured along*X*_{i}- α
_{i} The angle between

*Z*_{i}to*Z*_{ i+1}measured about*X*_{i}*d*_{i}The distance from

*X*_{i-1}to*X*_{i}measured along*Z*_{i}- θ
_{i} The angle between

*X*_{i-1}to*X*_{i}measured about*X*_{i}*p*_{x}, p_{y}, p_{z}End-effector coordinate of

*x, y, z*frame_{6}^{0}*T*Transform matrices from have to joint 6

*c*_{i}Cos θ

_{ i }*s*_{i}Sin θ

_{ i }*c*_{23}c

_{2}c_{3}-s_{2}s_{3}*s*_{23}c

_{2}s_{3}+s_{2}C_{3}*c*_{12}c

_{1}c_{2}-s_{1}s_{2}*s*_{12}c

_{1}s_{2}+s_{1}c_{2}*s*_{ϕ}s

_{123}- c
_{ε} c

_{123}- η
Learning rate

- α
Momentum term

- Δw
_{ij(t)} The weight matrices from

*i*.layer to*j*. layer variations after update*E(t)*Error variations for weights

- δ(
*t*) Derivation of error in weights

- \(\bar \delta (t)\)
Exponential average of past value of δ

- K
Constant value for learning rate

- φ
Correction factor of learning rate

- θ
Coefficient of the exponential average value

- μ
Maximum growth factor

*W*_{ij}Weight matrices from

*i*.layer to*j*.layer- N
Training numbers

*n*_{I}Number of neurons in the input layer

*n*_{H}Number of neurons in the hidden layer

*n*_{O}Number of neurons in the output layer

*z*_{j}(t)The output vector of the hidden layer

- AF
Activation function

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