KINEMATIC ANALYSIS OF ADEPT VIPER USING NEURAL NETWORK

Transcription

1 Proceedings of the National Conference on Trends and Advances in Mechanical Engineering, YMCA Institute of Engineering, Faridabad, Haryana., Dec 9-10, KINEMATIC ANALYSIS OF ADEPT VIPER USING NEURAL NETWORK Anurag Verma 1, Hiral H. Parikh 2 1 Department of Mechanical Engineering, G H Patel College Of Engineering & Technology, V.V. Nagar , Gujarat 2 Department of Mechanical Engineering, A. D. Patel Institute Of Engineering & Technology, New V.V. Nagar ,Gujarat 1,2 Phone: , , 1 Fax: , , 1,2 anuraganju@hotmail.com, dollyshah_3@yahoo.com Abstract Forward Kinematics is a fundamental problem of utmost importance in robot manipulator position control. Systematic and generalized approach for mathematical modeling of position and orientation of links in space with respect to a reference frame is established with help of vector and matrix algebra. In the present work forward kinematics based on artificial neural network using neuron model is evaluated with the help of MATLAB for analysis of a six link Adept Viper manipulator. The advantage of neural network used in Kinematics Analysis in context of computation ease, efficiency and tolerance is presented in this paper [1]. Key Words: Back propogation Algorithm, Feed Forward network, Artificial Neural Network 1.0 Introduction Over the past decade, the artificial intelligence community has undergone a resurgence of interest in the research and development of artificial neural networks. This paper begins with, 1) a general introduction to the Artificial Neural network [1], 2) a brief description of different neural network models, 3) a description of backpropogation learning Algorithm, and 4) D-H (Denavit Hartenberg) approach to do the mathematical modeling of Adept Viper, Followed by the training of the a network with the help of MATLAB programming. 2.0 Literature Review The correspondence between biological and artificial neuron is presented in the table [1]: Table 1. Comparison between Artificial and Biological network BIOLOGICAL TERMINOLOGY Neuron Synapse Synaptic Efficiency Firing Frequency NEURAL NETWORK TERMINOLOGY Node/Unit/Cell Connection/Edge/Link Connection Strength/Weight Node Output This paper focuses on a popular feedforward model of neural networks. In this model a set of inputs are applied to the network, and multiplied by a set of connection weights. All of the weighted inputs to the neuron are then summed and an activation function is applied to the summed value. This activation level becomes the neuron's output and can be either an input for other neurons, or an output for the network. Learning in this network is done by adjusting the connection weights based upon training vectors (input and corresponding desired output). When a training vector is presented to a neural net, the connection weights are adjusted to minimize the difference between the desired and actual output. After a network is trained with a set of training vectors, the network should produce a good output match for the inputs. The 3 basic elements of the neuronal model [1] are: 1) A set of the connecting links, each of which is characterized by a weight or strength of its own. Specifically a signal x j connected to the neuron K is multiplied by the synaptic weight W kj. It is denoted as W kj.the first subscript refers to the neuron in question and the second subscript refers to the input end of the synapse to which the weight refers. The synaptic weight of an artificial neuron may lie in a range that include negative as well as positive values. 1

2 2) An adder for summing the input signals, weighted by the respective synapse of the neuron. The operations described have constitute a linear combiner. 3) An activation function for limiting the amplitude of the output of a neuron. The activation function is also referred to as a squaring function. It squashes the permissible amplitude range of the output signal to some finite value. The neuronal model also includes an externally applied bias denoted by b k. The bias b k has the effect of increasing or lowering the net input of the activation function depending on whether it is positive or negative respectively. Input signal x 1 x 2 W k1 W k2 bia v k Function Φ(.) Output y k Sum w km x m weigh Fig1. General Neural Model In mathematical terms, we describe a neuron K by writing the following terms: U k =(w 11 x 1 +w 12 x 2 + w km x m ) (1) and Y k = ф( u k + b k ) (2) Where, x 1, x 2, x m are the input signals, W k j are the synaptic weights of neuron K, U k is the linear combiner output due to the input signals, B k is the bias, ф (.) is the activation function, y k is the output signal of the neuron. The general neural model can classify in different categories, like feed forward with no hidden layer, feed forward with multiple hidden layer with number of neuron in that layer. To train the network supervised learning and unsupervised learning method is available. In this paper supervised learning with Backpropogation Algorithm is used. 3.0 Problem Statement The ADEPT VIPER six link robot is used for pick and place application, The product from the one point has to be transferred to the other point accurately. Improper handling of the product can result in damage. Position of the robot manipulator has to be controlled properly for the better handling of the materials. P 4 P 3 P 2 P 1 P 5 P n 2

3 Proceedings of the National Conference on Trends and Advances in Mechanical Engineering, YMCA Institute of Engineering, Faridabad, Haryana., Dec 9-10, Adept Viper is used for pick and place application in the food industry. The part initially at the point P 1 has to reach to the point P n through the points P 2, P 3, P n-1. So, to transfer the product from the one point to the other point accurately some accurate method is required. In the present paper to control the position of robot neural network technique with Backpropogation Algorithm is used, once the network is trained for one set of training points it can simulate and also it is used to train the other set of training points. D 4 Z 4 Z 3 X 3 Z 6 X 6 Z 5 X 5 X 4 Z 2 X 1 X 2 A 3 Z 1 A 2 D 2 Z 0 X 0 Fig2. ADEPT VIPER Six link rotary joint robot [6] 4.0 Method For Forward Kinematics Solution: In the forward kinematics corresponding to the Joints angles with respect to the different link, position of end effectors has to be found out by D- H (Denavit Hartenberg) representation [3]. The D -H representation of a rigid link depends on four geometric parameters associated with each link. These four parameters completely describe any revolute or prismatic joint, that is shown in the table 2. Table 2. Link Coordinate parameter for ADEPT VIPER. JOINT θ i α i a i d i Joint range 1 θ to θ to 45 3 θ to θ to θ to θ to

4 With the help of D-H formulation following results obtained for ADEPT VIPER. Table 3. Forward kinematics Solution For ADEPT VIPER Manipulator θ ( ) 1 θ ( ) 2 ( ) θ 3 θ ( ) 4 θ ( ) 5 θ ( ) 6 P x P y P z From this Mathematical modeling now the neural network can be trained for forward kinematics solution with the help of Backpropogation Algorithm [4]. For training the network following parameters has to be decided initially [5]. 1. Input Function, 2. Output Function, 3. Training Function, 4. Performance Function, and 5. Learning Rate. In this paper following parameter has selected to train the network. 1. As Input Trainsigmoid function is used, 2. For the Output Pure linear function is used 3. To train the network trainscg (Scaled Conjugate Gradient ) function is used. This is optimization function. 4. Performance is evaluated in terms of Mean Square Error. 5. Learning rate is selected as 0.1 that indicate the increment in the weight in each step is ( initial weight +learning rate) FLOW CHART FOR TRAINING THE NETWORK TO CONTROL THE POSITION OF ADEPT VIPER. Start Choose the different sets of joint angles for all the links with the help of Table number 1. With the help of D-H formulation find the solution for forward kinematics (in terms of position vector) Write the program that train the network for the forward kinematics with the help of MATLAB toolbox Simulate the result End 4

5 5.0 Result Graphs Network Architectures Feed forward with no hidden layer Proceedings of the National Conference on Trends and Advances in Mechanical Engineering, YMCA Institute of Engineering, Faridabad, Haryana., Dec 9-10, Table 3.Results No of Epochs at which MSE mean square error. result obtain Feed forward with one hidden layer 5 neuron neuron Feed Forward network with no hidden layer 2. One hidden Layer with 5 neuron 5

6 3. One hidden layer with 10 neuron Here, the straight line (Linear line) indicating the target,and the Nonlinear line indicating the training process. As number of neuron increasing in the hidden layer training will become more complex. 6.0 Conclusion In the present paper from the above discussion, conclusions have been drawn as follows: 1. Faster Result than the iterative technique: Robot Positioning requires that the actuator positions are calculated as function of end effectors position. Some iterative methods are studied earlier and in this paper neural network approach is formulated for the same. The iterative methods are very time consuming while the neural network approach gives you faster results. 2. Time Saving process: Easy to develop the program for training the network. 3. Simulate for any training set of data: once the network is trained for any one set of teach point, the created network can also be used to simulate the data for other set of teach points. References 1. SIMON HAYKIN, 2003, Neural network -a comprehensive foundation 2. KISHAN MEHROTRA, CHILUKURI MOHAN, and SANJAY RANKA, 1997, Elements of artificial neural networks 3. K.S. FU, R.C.GONZALEZ, and, C.S.G.LEE, 1987, Robotics control, sensing, vision, and intelligence 4. B. YEGNANARAYANA PRENTICE,Artificial neural networks. 5. WILLIAM J. PALM, Introduction to matlab