Neural Network Model for Identifying Workspace, Forward and Inverse Kinematics of the 7-DOF YuMi 14000 ABB Collaborative Robot

13th IFAC Workshop on Intelligent Manufacturing Systems 13th IFAC IFAC Workshop Workshop on on Intelligent Intelligent Manufacturing Manufacturing Systems Systems 13th at www.sciencedirect.com August 12-14, 2019. Oshawa, CanadaAvailable online August 12-14, 2019. Oshawa, Oshawa, Canada August 12-14, 2019. Canada 13th IFAC Workshop on Intelligent Manufacturing Systems August 12-14, 2019. Oshawa, Canada

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IFAC PapersOnLine 52-10 (2019) 176–181

Neural Neural Network Network Model Model for for Identifying Identifying Workspace, Workspace, Forward Forward and and Inverse Inverse Kinematics of the 7-DOF YuMi 14000 ABB Collaborative Robot Neural Network Model for Identifying Workspace, Forward and Inverse Kinematics of the 7-DOF YuMi 14000 ABB Collaborative Robot Kinematics of the 7-DOF YuMi 14000 ABB Collaborative Robot

Morteza R. Morteza Alebooyeh*. Alebooyeh*. R. Jill Jill Urbanic** Urbanic**  Morteza Alebooyeh*. R. Jill Urbanic** Windsor, Windsor, Ontario, Canada N9B  *Department University  *Department of of Mechanical, Mechanical, Automotive, Automotive, and and Materials Materials Engineering, Engineering, University of of Windsor, Windsor, Ontario, Canada N9B 3P4; (e-mail: [email protected]). 3P4; (e-mail:Engineering, [email protected]). *Department of Mechanical, Automotive, and Materials University of Windsor, Windsor, Ontario, Canada N9B ** Department of Mechanical, Automotive, and Materials Engineering, University of Windsor, Windsor, Ontario, Canada N9B ** Department of Mechanical, Automotive, and Materials University of Windsor, Windsor, Ontario, Canada N9B 3P4; (e-mail: Engineering, [email protected]). 3P4 (e-mail: [email protected])} 3P4Materials (e-mail: [email protected])} ** Department of Mechanical, Automotive, and Engineering, University of Windsor, Windsor, Ontario, Canada N9B 3P4 (e-mail: [email protected])} Abstract: This research investigates development of a visual and analytical tool for the study of the Abstract: This research investigates development of a visual and analytical tool for the study of the seven degree of freedom (7-DOF) ABB 14000 YuMi robot.and It analytical provides an the Abstract: Thisofresearch investigates development of a visual toolunderstanding for the study of of the seven degree freedom (7-DOF) ABB YuMi robot. It provides an understanding the manipulator workspace regions where they14000 are visually represented for insight into the trueofwork seven degreeworkspace of freedom (7-DOF) ABB 14000 YuMi robot. It provides an understanding ofwork the manipulator regions where they are visually represented for insight into the true window. The developed tool is capable of realizing forward and inverse kinematics as well. The task is manipulator regions where of they are visually insight into the The truetask work window. Theworkspace developed tool is capable realizing forwardrepresented and inversefor kinematics as well. is achieved usingdeveloped artificial neural predictforward an inverse solution within an The acceptable window. tool is networks capable ofthat realizing andkinematic inverse kinematics as well. task is achieved The using artificial neural networks that predict an inverse kinematic solution within an acceptable confidence interval (90th-95th Mathematical models, including all i.e. achieved using artificial neural percentile). networks that predict an inverse withinmodels an acceptable confidence interval (90th-95th percentile). Mathematical models,kinematic includingsolution all kinematic kinematic models i.e. the the physical structure of manipulator joints and links, are developed and visually represented in physical structure manipulator joints Mathematical and links, aremodels, developed and all visually represented in the the confidence interval of (90th-95th percentile). including kinematic models i.e. MATLAB platform by using network MATLABstructure platform of by manipulator using the the neural neural network toolbox. physical joints and toolbox. links, are developed and visually represented in the MATLAB platform by using the neural network toolbox. © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Keywords: Collaborative Collaborative robots, robots, simulation, simulation, neural neural network, network, workspace, workspace, forward forward and and inverse inverse kinematics. kinematics. Keywords: Collaborative robots, simulation, neural network, workspace, forward and inverse kinematics.  (2013) have presented a technique to develop the functional  1. INTRODUCTION (2013) have presented a technique to develop the functional 1. INTRODUCTION and workspace of 66 DOF manipulators for and reachable reachable workspace of serial serial to DOF manipulators for (2013) have presented a technique develop the functional 1. INTRODUCTION determining the effective travel path regions. A work window Most manipulators used in the industry today are articulated and determining the effective travel path regions. A work window reachable workspace of serial 6 DOF manipulators for Most in the industry todaystructural are articulated the FANUC 6R has along with manipulators six or more used rotational joints. This form algorithm algorithm for forthe theeffective FANUCtravel 6R family family has been beenAprovided provided along path regions. work window Most manipulators used in the industry todaystructural are articulated with six or more rotational joints. This form determining with singularity visualization for certain manipulator provides the manipulators with a great deal of flexibility, with singularity visualization for certain manipulator algorithm for the FANUC 6R family has been provided along with six the or manipulators more rotational This form configuration(s). Work done by Urbanic (2012) has presented provides withjoints. a great dealstructural of flexibility, dexterity, and manipulators an ability to reach specific coordinate of with singularity visualization for certain manipulator provides with every a great deal of flexibility, done by Urbanic (2012) presented dexterity, the and an ability to reach every specific coordinate of configuration(s). an estimation of Work the functional workspace of ahas manipulator their workspace in more than one configuration (Aggarwal Work done by Urbanic (2012) has presented an estimation of the functional workspace of a manipulator their workspace moretothan configuration (Aggarwal dexterity, and an in ability reachone every specific coordinate of configuration(s). using kinematic modelling and workspace shape analyses. The outer 2014). Positioning manipulator aa work critical estimation of the functional of a manipulator using kinematic modelling and shape analyses. The outer 2014).workspace Positioning manipulator in configuration work cell cell is is(Aggarwal critical to to an their in aamore than onein boundary curves for an ABBand IRB-140 has outer been ensure accessibility the intended kinematic modelling shape manipulator analyses. The boundary curves for an ABB IRB-140 manipulator has been ensure Positioning accessibilityafor for the tasks tasks and and processes itisis iscritical intended 2014). manipulator in aprocesses work cellit to using assessed for functional workspace of a desired end-effector to An mapping from Cartesian to curves for an workspace ABB IRB-140 has been assessed for functional of amanipulator desired end-effector to serve. serve. An inverse inversefor mapping from the Cartesian space to aa boundary ensure accessibility the tasks andthe processes it isspace intended and tool orientation. Advantages of this technique include an manipulator’s joint space is thus required and is a challenging and tool orientation. Advantages of this technique include an assessed for functional workspace of a desired end-effector to serve. An inverse mapping the Cartesian space to a understanding of the joint reach feasibility prior to on-site manipulator’s space is thusfrom required and is such a challenging aspect of robotjoint control. Numerous techniques as teach and understanding of the joint reach feasibility prior to on-site tool orientation. Advantages of this technique include an manipulator’s joint spaceNumerous is thus required and is such a challenging aspect of robot techniques as teach Djuric and pendants, robot control. simulation software, manual trial and error setups setups in in aa manufacturing manufacturing environment. Djuric andtoUrbanic Urbanic of the joint environment. reach feasibility prior on-site aspect of robot Numerous techniques suchand as teach pendants, robot control. simulation software, manual trial error understanding (2012) have presented a similar technique for building field tests, etc. are currently used in industry for determining setups in a manufacturing environment. Djuric and Urbanic pendants, robot simulation software, manual trial and error (2012) have presented a similar technique for building field tests, etc. are currently used in industry for determining reconfigurable alternatives and assessing the systems design joint that produce aa required pose have presented a and similar technique for building field tests, etc. are currently in industry for tool determining reconfigurable assessing systems design joint configurations configurations that may may used produce required tool pose for for (2012) through the usealternatives of functional workspace ofthe manipulators. The ajoint task. All these techniques utilize conventional geometric, assessingofthe systems design through the usealternatives of functionaland workspace manipulators. The a task. All these techniques utilize conventional geometric, configurations that may produce a required tool pose for reconfigurable work window has been graphically mapped at different tool iterative or analytical methods to aa solution to the usehas of functional workspace of manipulators. work window been graphically mapped at different The tool or these analytical methods to develop develop solution to the the through aiterative task. All techniques utilize conventional geometric, orientations to compare the feasibility of operations for problem positioning aa manipulator’s end-effector. orientations compare the feasibility of atoperations for windowtohas been graphically mapped different tool problem for for positioningmethods manipulator’s end-effector. Often, iterative or analytical to develop a solution Often, to the work multiple kinematic chains in a manufacturing cell. the development of a closed form solution to this problem multiple kinematic chains in a manufacturing cell. orientations to compare the feasibility of operations for problem for positioning a manipulator’s end-effector. Often, the of a closed form solution to this problem maydevelopment be mathematically complex and computationally kinematic chains a manufacturing cell. the development of a closedcomplex form solution to this problem multiple Kozakiewicz (1991) hasin proposed a partitioned neural may be mathematically and computationally expensive or may not even be possible. These limitations can Kozakiewicz (1991) has proposed a partitioned neural may be or mathematically architecture to improve the accuracy for an inverse expensive may not even becomplex possible. and Thesecomputationally limitations can network network architecture improve the accuracy for an inverse (1991) tohas proposed a partitioned neural be overcome by the of non-traditional approaches such as Kozakiewicz expensive or may notuse even be possible. These limitations problem. The networktheachieved prediction be overcome by the use of non-traditional approaches suchcan as kinematic network architecture to improve accuracyhigh for an inverse Artificial Neural Networks (ANNs). ANNs can identify and kinematic problem. The network achieved high prediction Artificial Neural Networks (ANNs). ANNs can identify be overcome by the use of non-traditional approaches suchand as accuracy for the position joints but exhibited higher errors for kinematicfor problem. The joints network achieved higher high prediction predict trends amongst data sets with an thejoints. position buthas exhibited for predict non-linear non-linear trends (ANNs). amongstANNs data can setsidentify with and an accuracy the orientation Lou (1999) introduced anerrors iterative Artificial Neural Networks accuracy for thejoints. position joints buthas exhibited higher errors for acceptable level of accuracy which makes them suitable for the orientation Lou (1999) introduced an iterative acceptable level of accuracy which makes predict non-linear trends amongst datathem setssuitable with for an approach for computing the(1999) inversehas kinematic problem using the orientation joints. Lou introduced an iterative such an application (Aggarwal 2014). approach for computing the inverse kinematic problem using such an application 2014).makes them suitable for ANNs acceptable level of (Aggarwal accuracy which with offset method to approach foran thecompensation inverse kinematic problem using ANNs with ancomputing offset error error compensation method to improve improve such an application (Aggarwal 2014). the accuracy of the derived solution. The methodology has Significant research has been dedicated towards the ANNs the accuracy of the derived solution. The methodology has with an offset error compensation method to improve Significant researchmanipulators. has been Most dedicated the been implemented since an offset error, which had different modelling industrial of this towards research has been implemented since an offset error, which had different the accuracy of the derived solution. The methodology has Significant researchmanipulators. has been Most dedicated towards has the modelling of this for each required end-effector position, always existed focused onindustrial the development and optimization of research manipulator values values for each required end-effector position, always existed been implemented since an offset error, which had different modelling manipulators. Most of this has focused onindustrial the development and optimization of research manipulator taking iterative approach. Bingulalways (2005) has design and in anand industrial setting.ofGoyal (2010) when for eachthe required end-effector position, existed focused on functionality the development optimization manipulator when taking iterative approach. Bingul (2005) design and functionality in an industrial setting. Goyal (2010) values explored threethe different end-effector orientation types has for has determined the workspace of an RV-M1 Mitsubishi taking the iterative approach. orientation Bingul (2005) has design and functionality in an industrial Goyal (2010) when explored threeANN. different end-effector types for has determined the workspace of an setting. RV-M1 Mitsubishi training an The method is validated on a 6R manipulator modelled using (DH) explored an threeANN. different types The end-effector method is orientation validated on a for 6R manipulator modelled using Denavit-Hartenberg Denavit-Hartenberg (DH) training has determined the workspace of an RV-M1 Mitsubishi manipulator with a wrist offset. The results are satisfactory parameters use MATLAB’s robotics The an with ANN. The offset. methodTheis results validated on a 6R manipulator a wrist are satisfactory parameters through through use of ofusing MATLAB’s robotics toolbox. toolbox.(DH) The training manipulator modelled Denavit-Hartenberg with high 10 degrees of resolution. ANNs paper the of manipulator with errors errors as aswith higha as as 10 offset. degreesThe of data data resolution. ANNs wrist results are satisfactory paper has has emphasized emphasized that the workspace workspace of aa toolbox. manipulator parameters through use that of MATLAB’s robotics The manipulator provide a quicker response and have proven to be useful for impacts its design, placement, and dexterity. Djuric et al. provide a quicker response and have proven to be useful for with errors as high as 10 degrees of data resolution. ANNs paper hasitsemphasized that the workspace of aDjuric manipulator impacts design, placement, and dexterity. et al. multiple satisfactory solution(s) to the inverse kinematics multiple satisfactory solution(s) to the inverse kinematics provide a quicker response and have proven to be useful for impacts its design, placement, and dexterity. Djuric et al. 2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting Elsevier Ltd. All rights reserved. multipleby satisfactory solution(s) to the inverse kinematics

Copyright@ 2019 IFAC 176Control. Peer review under responsibility of International Federation of Automatic Copyright@ 2019 IFAC IFAC 176 Copyright@ 2019 176 10.1016/j.ifacol.2019.10.019 176 Copyright@ 2019 IFAC

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problem with real-time adaptive control (Köker (2004) and Hasan 2010). An inherent challenge with this technique has been related to increasing the developed network’s accuracy.

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the left arm of the cobot, and as presented in Table 2, and Figure 4, respectively.

Research carried out, however, does not consider a versatile model for 7-DOF articulated robot manipulators. A need is therefore recognized for the development of a tool that can generate and identify feasible workspace topologies for a 7DOF YuMi collaborative robot (cobot), which is the focus of this paper. 1.1 7-DOF YuMi 14000 ABB Industrial Robot The YuMi dual arm robot (Figure 1) has a vision system, controllable dexterous grippers (speed and gripper position), sensitive force control feedback, flexible software and builtin safety features that collectively allow for programming through teaching rather than coding. The design and performance characteristics are summarized in Table 1. Fig. 2. YuMi robot arm links and joints (Robotics product specification IRB 14000, 2015).

Fig. 1. 7-DOF YuMi 14000 ABB Industrial Robot.

Fig. 3. YuMi robot free body diagram (Robotics product specification IRB 14000, 2015).

Table 1. YuMi characteristics (Robotics product specification IRB 14000, 2015) Feature Degrees of Freedom Large working range Linear speed of gripping operation Max Force of Gripper Payload (Max load for each arm) Max TCP Velocity Width, Length, Height Weight

Table 2. DH parameters for the left arm (i is the axis)

Value 7 per side 559 mm 0.25 mm/sec 20 N 500 gr 1.5 m/s 399*497*571 38 Kg

lower upper theta a (link alpha (link joint joint (link twist) length) angle) limit limit 1 D1=166 0 A1=-30 -90 -168.5 168.5 2 D2=0 0 A2=30 90 -143.5 43.5 3 D3=251.5 0 A3=40.5 -90 -123.5 80 4 D4=0 -90 A4=40.5 -90 -290 290 5 D5=265 180 A5=27 -90 -88 138 6 D6=0 0 A6=-27 90 -229 229 7 D7=36 0 A7=0 0 -168.5 168.5 The robot link’s characteristics for each joint i and the range of motion for each joint is italicized in Table 2. i

This cobot has a compact frame and 14-axes (2-7 serial axis with rotary joint configurations). The type of motion for Axis 1 and 7 is rotation motion by arms while axis 2 and 3 involve bend motion by arms. Axis 4 and 5 have rotation and bend motion, respectively, using wrists and finally, axis 6 has rotation motion using a flange. It is a portable robot with lightweight padded arms, and multifunctional hands. It is fast and highly accurate (returning to the same point in space to within 0.02 mm accuracy) with sophisticated speed limited motion technology (Figures 2 to 4). Figure 3 shows free body diagram of YuMi IRB 14000 robot. The robot’s teach pendant and RobotStudio software has been used to extract lower and upper joint limits as well as the DH parameters for

d (link offset)

2. METHODOLOGY 2.1 Neural Network Model Artificial neural networks are flexible, adaptive learning systems that follow the observed data to find patterns and develop nonlinear models to make predictions. Their key features are: they process information locally in neurons; neurons operate in parallel and are connected into a network 177

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through weights; networks acquire knowledge from the input by learning, which is stored or reflected in the weights; and earned network captures essential features of a problem and can make predictions.

learning technique based of the Gradient Descent and Newton’s method (Equation 2). (2)

𝛥𝛥𝑤𝑤𝑚𝑚= − 𝑑𝑑𝑚𝑚/(𝑑𝑑𝑚𝑚s+ 𝑒𝑒𝜆𝜆)

where, 𝑑𝑑𝑚𝑚 is the first derivative of error, is the second derivative of error, and λ is the damping factor. Validation stops have been disabled by default (max fail = inf) so that training can continue until an optimal combination of errors and weights is found. Bayesian Regulation can train any network as long as its weight, net input, and transfer functions have derivative functions (Foresee 1997). 𝑑𝑑𝑚𝑚𝑠𝑠

2.3 Activation Function Activation functions help the weights in the network identify and learn trends in a dataset. These functions can help introduce non-linearity into the network which allows the network to process complex, and non-linear datasets. The hyperbolic tangent function has been used as the activation function for the network’s hidden layer (Equation 3). Unlike the logistic function, this function is beneficial when the data set to be trained has both positive and negative values in its input and target dataset. The data should be normalized before being fed to the network for improved performance.

(a)

tanh(𝑢𝑢)= 1−𝑒𝑒−2𝑢𝑢/1+ 𝑒𝑒−2𝑢𝑢

(3)

where, β is the slope parameter, and u is any value from a dataset. The output from a neuron using any activation function, f, is given by Equation 4.

(b)

𝑁𝑁𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 = f (Σ𝑤𝑤𝑗𝑗𝑥𝑥𝑗𝑗+𝑏𝑏)

Fig. 4. (a) YuMi left arm configuration, and (b) MATLAB model (units are in mm).

(4)

The output layer uses a linear activation function given by 𝑓𝑓(𝑢𝑢)= 𝑢𝑢 as its processing unit. Unlike the hyperbolic tangent function, the linear activation function does not constrain the data but rather scales it linearly. This helps attain a true output value with respect to the network input.

In this study a feed-forward back-propagation batch learning algorithm with multilayer perceptron (MLP) neural network model has been employed because of its capability to perform complex prediction with a supervised learning technique.

2.4 Data Pre-processing and Post Processing 2.2 Training

Normalization has been used for this solution approach. D-H parameters often have a different scale than the joint variable ranges. The difference in scale may mask the effect of one variable on another. Normalization of data is therefore essential to scale all input and target datasets in a pre-defined range. The pre-defined range used for training the network is [-1, 1]. This guarantees a stable convergence of weights and biases. Normalization also helps to identify the true effect of any one variable on another variable. Two normalization techniques, namely, min-max normalization (Equation 5) and z-score normalization have been applied to the dataset(s) used for training the network.

Back-propagation of the error allows the network to calculate the error at each output and adjust the value of the weights that caused the error, thereby reducing the overall error in the network. The error indicator considered for the network performance is the mean squared error (MSE) value. The MSE value determines the accuracy of prediction over all the training patterns for a given network (Equation 1). 𝐸𝐸= 1/2𝑁𝑁(Σ(𝑡𝑡𝑖𝑖−𝑧𝑧𝑖𝑖 )2) )

(1)

where, E is the MSE value, 𝑡𝑡𝑡𝑡 is the target for the ith training pattern, 𝑧𝑧𝑧𝑧 is the predicted output for the ith training pattern, and N is the total number of training patterns. The Bayesian Regulation backpropagation learning algorithm has been used to adjust and update the weights of the network. It is a network training algorithm that updates the weight and bias values according to Levenberg-Marquardt (LM) optimization. It minimizes a combination of squared errors and weights, and then determines the correct combination to produce a network that generalizes well. LM is a hybrid

𝑋𝑋′=(𝑎𝑎+(𝑋𝑋−𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚)(𝑏𝑏−𝑎𝑎))/𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚−𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚

(5)

where, 𝑋𝑋 denotes any value in the data set, 𝑋𝑋′ denotes the normalized value of 𝑋𝑋, a = -1, b = 1, 𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚 𝑎𝑎𝑎𝑎𝑎𝑎 𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚 are the maximum and minimum values in the dataset respectively. The network outputs from a normalized input set are also normalized. All values in the output data set therefore need to be reverted to scale. The scale for de-normalizing an output 178

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dataset is determined from the range of target dataset supplied to the network.

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chosen. The accuracy with a smaller step size has been increased because of the reduced level of complexity in the dataset. The computation time of the network has been also decreased substantially with this approach. The values in a range have been randomized to prevent formation of classes in a continuous dataset. The model forms the manipulator’s joint space by making all possible combinations of each joint variable. For a 7-DOF manipulator, the total combinations of 7 joints will be 2187 (3^7). These joint configurations would provide 2187 Cartesian coordinates that have been represented as the complete workspace.

The ANNs for this research have been developed with the aid of the Graphical User Interface (GUI) Neural Network (NN) Toolbox in the MATLAB environment. For training a network, all data has been divided at random into three mutually exclusive and collectively exhaustive categories, including the training set, the validation set, and the testing set accounting for 90% 5% and 5% of the original data, respectively, selected at random by the NN Toolbox. This data division percentage of 90-5-5 has been selected since the ANN yielded a better performance when compared to the default configuration (70-15-15). This is because the network is able to train over a larger dataset range while the validation and testing dataset performance remained constant.

3. Inverse Kinematics Solution: The position and orientation of each point in the manipulator workspace defines the inputs for the inverse kinematics ANN model. The corresponding joint space of the network inputs defines the network targets.

2.5 Network Prediction Capability

2.7 Generalization and Accuracy of the ANN Model

Network outputs are the predicted values from the trained network, which are compared with the known targets for errors in prediction. The relative percentage error for the prediction has been calculated for a target dataset with no zero values, subtracting the output from a target and dividing the result over target. If the target dataset contains values that are zero, a percentage error cannot be computed since the numerator would require division with 0. In such cases, the absolute error has been computed.

A challenge with ANN models is the accuracy of a developed network. An acceptable level of accuracy is needed to make confident predictions. For improving generalization, the network’s DOF need to be lowered, which is achieved by reducing the number of free parameters, or the weights to each hidden neuron. These hidden neuron weights are directly proportional to the flexibility of the network (Samarasinghe 2007). Using trial and error, it has been observed that an ANN with 75 neurons in one hidden layer provides the optimal network generalization and accuracy.

2.6 Inverse Kinematics using Neural Networks

3. RESULTS AND ANALYSIS

The network architecture uses a 12 input dataset which represent the position of the end-effector (𝑝𝑝𝑝𝑝,𝑝𝑝𝑝𝑝,𝑝𝑝𝑝𝑝), and the orientation of the end-effector (𝑛𝑛𝑛𝑛,𝑛𝑛𝑛𝑛,𝑛𝑛𝑛𝑛,𝑏𝑏𝑏𝑏,𝑏𝑏𝑏𝑏,𝑏𝑏𝑏𝑏,𝑡𝑡𝑡𝑡,𝑡𝑡𝑡𝑡,𝑡𝑡𝑡𝑡) from the forward kinematics (Equation 6). The targets and network outputs are the configurations of the joint variables (𝑞𝑞1,𝑞𝑞2,𝑞𝑞3,𝑞𝑞4,𝑞𝑞5,𝑞𝑞6,q7) that produce the input position and orientation.

The best validation performance, as seen from Figures 5 and 6, has been obtained at epoch 1000. The network training has been completed at epoch 1000 since validation stops have been disabled so that training can continue until an optimal combination of errors and weights is found.

(6)

The mathematical model has been built for the YuMi cobot using the NN MATLAB toolbox. The mathematical model requires D-H Parameters and the range of motion for all joint variables as inputs. Based on inputs, the model successfully computes and evaluates the following outputs: 1. Forward Kinematics Solution: Due to the unavailability of inverse kinematic solution(s) for most industrial manipulators, a forward kinematics solution has been first developed to lead to outputs that will be subsequently served as input data set in inverse kinematics. Thus, the model first computes all individual homogenous transformation matrices to be subsequently used to develop a forward kinematics homogeneous matrix.

Fig. 5. ANN Architecture for the YuMi robot. The regression plot in Figure 7 demonstrates a good fitness between the network outputs and the target values. A perfect fit is indicated by a regression (R) value of 1. A comparison between the network outputs and targets (joint

2. 3-D Workspace: The model starts by splitting the range of each joint variable into three values. A step size of 3 provided the most accurate ANN model results over any other step size 179

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configurations) is presented in Figure 8. The network is very accurate in predicting joints 2, 3, 5 and 7 for the manipulator. It can be observed that the predicted outputs of the network almost superimpose onto the target values. However, some variation can be observed in joints 1, 4 and 6 which are either high range or belong to the manipulator wrist.

accuracy of prediction. The individual performance values for the training, testing, and validation dataset are low and are around the generated MSE value as well. The error histogram in Figure 9 illustrates the frequency of errors concentrated over a range. A well fit network has the maximum frequency of errors around zero. In the network trained for YuMi robot, the maximum errors in all training, validation, and testing dataset are mostly concentrated between -0.23 to 0.13. The error histogram displays a good normal distribution.

Fig. 6. Performance plot for YuMi robot NN.

Fig. 8. Inverse kinematics predictions for the NN model.

Fig. 9. Error histogram for the YuMi robot NN model. Fig. 7. Regression Plot for YuMi robot NN model. The complete 3-D workspace of the manipulator has been represented in Figure 10. The Cartesian space configuration of this subset workspace has been normalized and provided to the network as inputs. The joint angle configurations have been normalized and provided as targets.

This variation arises due to the generalization properties of the developed ANN. The purpose of an ANN is to determine a generalized trend between the input and output parameters of a given manipulator, rather than mapping exact points which leads to an over-fitted model. It is important to realize that multiple wrist configurations may exist for every given set of position coordinates (X,Y,Z) in the input data set. These wrist configurations primarily contribute to the orientation of the manipulator’s end-effector. For each set of unique position coordinates, the wrist can therefore assume a specific set of joint configurations. As a result, during the training phase, the ANN network attempts to predict a generalized model for Joints 4 and 6. Hence, when a new input set of parameters is introduced to the network, the network attempts to predict an overall generalized result for these joints based on their average thereby reducing network accuracy. The network performance indicator, MSE, has an appropriate value of 0.32. A low MSE value indicates a good 180

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Fig. 10. Total workspace (reach conditions) for the YuMi robot NN model.

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Conditions for Articulated Robots and Machine Tools, MSc Thesis, University of Windsor. Bingul, Z., Ertunc, H., and Oysu, C. (2005). Comparison of inverse kinematics solutions using neural network for 6R robot manipulator with offset. ICSC Congress on Computational Intelligence Methods and Applications, Istanbul. Djuric, A. and Urbanic, R.J. (2012). Utilizing the Functional Work Space Evaluation Tool for Assessing a System Design and Reconfiguration Alternatives. Robotic Systems - Applications, Control and Programming, Dutta. Djuric, A., Urbanic, R.J., Filipovic, M. and Kevac, L., (2013). Effective Work Region Visualization for Serial 6 DOF Robots. 5th International Conference on Changeable, Agile, Reconfigurable and Virtual Production (CARV), Munich. Foresee, F.D. and Martin T.H. (1997). Gauss-Newton approximation to Bayesian learning. Proceedings of the International Joint Conference on Neural Networks. Goyal, K. and Sethi, D. AN ANALYTICAL METHOD TO FIND WORKSPACE OF A ROBOTIC MANIPULATOR. Journal of Mechanical Engineering, volume (41), 25-30. Hasan, A.T., Ismaila, N.A., Hamoudab, A., Ishak, M.H., and Al-Assadia, H. (2010). Artificial neural network-based kinematics Jacobian solution for serial manipulator passing through singular configurations. Advances in Engineering Software, volume (41), 359-367. Köker, R., Öz, C., Çakar, T. and Ekiz, H. (2004). A study of neural network based inverse kinematics solution for a three-joint robot. Robotics and Autonomous Systems: Patterns and Autonomous Control, volume (49), 227234. Kozakiewicz, C., Ogiso, T. and Miyake, N. (1991). Partitioned neural network architecture for inverse kinematic calculation of a 6 DOF robot manipulator. IEEE International Joint Conference on Neural Networks. Lou Y.F. and Brunn P. (1999). A hybrid artificial neural network inverse kinematic solution for accurate robot path control. Journal of System and Control Engineering, volume (213), 23-32. Robotics Product specification IRB 14000, Revision: J, ABB AB, Robotics and Motion Se-721 68 Västerås, Sweden, 2015 Samarasinghe, S. (2007). Neural Networks for Applied Sciences and Engineering: From Fundamentals to Complex Pattern Recognition, Taylor and Francis Group, Boca Raton. Urbanic, R.J. and Gudla, A. (2012). Functional Workspace Estimation of a Robot using Forward Kinematics, D-H Parameters, and Shape Analyses. ASME 11th Biennial Conference on Engineering Systems Design and Analysis, Nantes.

A summary of the ANN inverse kinematic results is provided in Table 3. Table 3. ANN Results for ABB 14000 YuMi Robot ANN Network Indicator Result Total Epochs 1000 Epoch for Best Validation Performance 1000 Overall Regression (R) Value 0.714 Mean Square Error (MSE) 0.31987 Training Performance 0.3064 Testing Performance 0.4686 Validation Performance NaN Error Histogram Center (Bell Curve) -0.05153 Figure 11 illustrates a plot of absolute residual errors between the aforementioned networks outputs and targets due to the network generalization.

Fig. 11. Absolute residual error for the inverse kinematics prediction for the YuMi robot NN model. 4. SUMMARY AND CONCLUSIONS A neural network model has been developed to gain an insight into the functionality of 7-DOF YuMi industrial robot and optimization of its performance. The developed model is successfully able to provide a forward kinematics solution, an inverse kinematic solution and a 3D visual representation of workspace. This model can be successfully used for optimizing the placement of the YuMi industrial robot in an industrial setting and understanding its reach conditions based on an analysis of its functional workspace. The MATLAB programming based developed tool aids to further research in the field of industrial robotics. It also helps robot designers, manufacturers, as well as end-users to understand the true functionality and capabilities of any manipulator. The research can ultimately be extended to incorporate complex robot structures such as parallel link manipulators etc. REFERENCES Aggarwal, L. (2014) Reconfigurable Validation Model for Identifying Kinematic Singularities and Reach

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