Transcript
Noise analysis of robot manipulator using neural networks S - ahin Yildirim n , _ Ikbal Eski Erciyes University, Faculty of Engineering, Mechanical Engineering Department, Kayseri 38039, Turkey a r t i c l e i n f o Article history: Received 5 November 2007Received in revised form14 September 2009Accepted 13 October 2009 Keywords: NoiseRobot manipulatorNeural networkRobust neural noise analyzer a b s t r a c t Due to a lot of robot manipulators application in industry, low noise degree is very important criteria forrobot manipulator’s joints. In this paper, joint noise problem of a robot manipulator with five joints isinvestigated both theoretically and experimentally. The investigation is consisted of two steps. Firststep is to analyze the noise of joints using a hardware and software. The hardware is a part of noisesensors. The second step; according to experimental results, some neural networks are employed forfinding robust neural noise analyzer. Five types of neural networks are used to compare each other.From the results, it is noted that the proposed RBFNN gives the best results for analyzing joint noise of the robot manipulator. & 2009 Elsevier Ltd. All rights reserved. 1. Introduction Neural network as a predictor has been widely used in theprocess and robotic handling industries because it is robust.Neural networks have been employed in various ways toconstruct nonlinear systems to handle a variety of controlobjectives. Typically, the key elements in their design procedureare the proper choice of the functions to be approximated and anappropriate control strategy that utilizes this approximation.However, these strategies usually require the neural network-based approximation to be sufficiently accurate.Robot manipulators have become increasingly important inthe field of flexible automation and manufacturing system inindustrial applications such as material handling [1]. Program-mability, high speed and high precision are some of the goodqualities they possess which are desirable for flexible automation.Vibration analysis of robot manipulators has been investigated byseveral researchers. Cheong and Youm [2] have proposed thesystem mode analysis of horizontal vibration for 3-D two-linkflexible manipulators. For the analysis, the authors have for-mulated and solved a set of partial differential equations whichrepresent vibration mixed with bending and torsional moment. Intheir research, an examination and comparison between the two joint conditions have been performed. Numerical and experi-mental tests have showed the validity and effectiveness of theproposed analysis and modeling. Cheong et al. [3] have suggestedthe accessibility of horizontal vibration in a 3-D two-link flexiblerobot shows configuration-dependent nature. The analysis of horizontal vibration based on system mode approach takes animportant role in examining the vibration accessibility. Boththeoretical and numerical studies were presented to elucidate themeaning of the accessibility and the identifiability of horizontalvibration. In addition, the experimental results support thetheoretical results.An effect of flexibility on the trajectory of a planar two-linkmanipulator has studied using integrated computer-aided design/analysis (CAD/CAE) procedures [4]. Chu et al. [5] have proposed a new type of stepping piezoelectric micro-motor using wigglevibration mode and three-dimensional contacts between the rotorand stator. A hybrid input shaping method to reduce the residualswing of a simply suspended object transported by a robotmanipulator or the residual vibration of equivalent dynamicsystems has been studied by Kapucu et al. [6].A 3-PPR planar parallel manipulator, which consists of threeactive prismatic joints, three passive prismatic joints, and threepassive rotational joints, has been proposed [7]. The analysis of the kinematics and the optimal design of the manipulator havealso been discussed and an example using the optimal design wasalso presented.A neural network has employed to analyze of inversekinematics of PUMA 560 type robot [8]. Callegari et al. [9] have presented the inverse dynamics model of a novel translatingparallel machine and proposes the structure of a force controllerfor the execution of tasks characterized by interaction with theenvironment. The effect of miniaturization on two dynamic andtwo quasi-static motion mechanisms has been experimentallyevaluated using a miniature piezoceramic drive unit [10]. A newapproach to the dynamic motion planning problems of mobilerobots in uncertain dynamic environments based on the behaviordynamics from a control point of view was provided [11]. The ARTICLE IN PRESS Contents lists available at ScienceDirectjournal homepage: www.elsevier.com/locate/rcim Robotics and Computer-Integrated Manufacturing 0736-5845/$-see front matter & 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.rcim.2009.10.001 n Corresponding author. E-mail address:
[email protected] (S - . Yildirim).Robotics and Computer-Integrated Manufacturing 26 (2010) 282–290 ARTICLE IN PRESS purpose of this paper is to obtain a neural network vibrationanalyzer and develop a robust neural network model for robotmanipulator’s end-effector under big payload conditions.This paper is organized as follows: Section 2 describes thetheory of robot manipulators. Section 3 gives some details aboutneural networks and the proposed neural network. The experi-mental results and discussions are given in Section 4. Finally, thispaper is concluded with conclusions and discussion. 2. Robot manipulator In this work, five degrees of freedom an industrial robotmanipulator is employed for analyzing vibration parameters of joints are shown in Figs.1 and 2. The robot manipulator’s jointsare driven by servo motors for that reason; maximum speed of robot manipulator’s end-effector is 2200 mm/s (see Table 1). Thepositioning repetition accuracy of the robot manipulator is 7 0.02 mm. The maximum reach ability of the robotmanipulator’s end-effector is 410 mm. When the Newton–Eulerequations are evaluated for five-link robot manipulator, dynamicequation can be written in the following form: t ¼ M ð H Þ € H þ V ð H ; _ H Þþ G ð H Þ ð 1 Þ where M ( H ) is the n n mass matrix of the manipulator V ð H ; _ H Þ is the n 1 vector of centrifugal and Coriolis terms, G ( H ) is an n 1 vector of gravity terms ( n =5). Each element of M ( H ) and G ( H ) is a complex function which depends on H , the position of all the joints of the manipulator. Each element of V ð H ; _ H Þ is acomplex function of both H and _ H .The dynamics of the robot manipulator with respect toCartesian variables can be expressed in the following form: F ¼ M x ð H Þ € X þ V x ð H ; _ H Þþ G x ð H Þ ð 2 Þ where F is a force-torque vector acting on the end-effector of therobot, and X is an appropriate Cartesian vector representingposition and orientation of the end-effector. Analogous to the joint space quantities, M x ( H ) is the Cartesian mass matrix, V x ð H ; _ H Þ is a vector of velocity terms in Cartesian space, and G x ( H ) is a vector of gravity terms in Cartesian space. Note that thefictitious forces acting on the end-effector, F , could in fact be Fig. 1. Experimental System Setup. Nomenclature a I ( i ) the output of competitive layer b j the bias of the j th neuron in the hidden layer b k the bias of the kth neurons in the output layer c the Coulomb friction constant E 1 ( t ) the error between experimentally and neural networkoutput signals E 2 ( t ) the propagation error between hidden layer andoutput layer f the input vector F the force-torque vector g ( ) activation function g j the normalized output vector elements of the gatingnetwork G ( H ) the vector of gravity terms G x ( H ) the vector of gravity terms in Cartesian space J ( H ) the Jacobian matrix K the number of local networks M ( H ) the mass matrix of the manipulator M x ( H ) the Cartesian mass matrix N training numbers n number of joints N f the experimentally obtained number of cycles tofailure N fn the corresponding neural network 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 r j the radius vector of the j th hidden unit T the target values v the viscous friction constant V ð H ; _ H Þ the vector of Coriolis terms V x ð H ; _ H Þ the vector of velocity terms in Cartesian space y j the output of the j th local network W jk the weights between j th neurons hidden layer and k thneurons output layer W ij the weights between i th neurons input layer and j thneurons hidden layer X the appropriate Cartesian vector representing posi-tion and orientation of the end-effector Z j ( t ) the output vector of the hidden layer Z learning rate a momentum term D W ij ð t Þ the weight variations matrices from i layer to j layerafter update D W jk ð t Þ the weight variations matrices from j layer to k layerafter update S. Yildirim, I Eski / Robotics and Computer-Integrated Manufacturing 26 (2010) 282–290 283 ARTICLE IN PRESS applied by the actuators at the joints using the relationship s ¼ J T ð H Þ F ð 3 Þ where the Jacobian, J ( H ), is written in the same frame as F and € X ,usually the tool frame, { T }. The inverse of the Jacobian transposeto obtain J T s ¼ J T M ð H Þ € H þ J T V ð H ; _ H Þþ J T G ð H Þ ð 4 Þ or F ¼ J T M ð H Þ € H þ J T V ð H ; _ H Þþ J T G ð H Þ ð 5 Þ The relationship between joint space and Cartesian accelera-tion has been developed and starting with the definition of the Jacobian, € X ¼ J _ H ð 6 Þ and differentiating to obtain € X ¼ _ J þ J € H ð 7 Þ Solving (7) for joint space acceleration leads to € H ¼ J 1 € X J 1 _ J _ H ð 8 Þ Substituting (8) into (5) F ¼ J T M ð H Þ J 1 € X J T M ð H Þ J 1 _ J _ H þ J T V ð H ; _ H Þþ J T G ð H Þ ð 9 Þ from which the expressions for the terms in the Cartesiandynamics has been derived, M x ð H Þ ¼ J T ð H Þ M ð H Þ J 1 ð H Þ V x ð H ; _ H Þ ¼ J T ð H Þ½ V ð H ; _ H Þ M ð H Þ J 1 ð H Þ _ J ð H Þ _ H ð 10 Þ G x ð H Þ ¼ J T ð H Þ G ð H Þ Fig. 2. (a) Schematic description of robot manipulator and (b) gripper of end-effector of the robot manipulator. S. Yildirim, I Eski / Robotics and Computer-Integrated Manufacturing 26 (2010) 282–290 284 ARTICLE IN PRESS The Jacobian appearing in Eq. (10) is written in the same frameas F and X in (2) though the choice of this frame is arbitrary. Notethat when the manipulator approaches a singularity, certainquantities in the Cartesian dynamics become infinite.In order to make dynamic equations reflect the reality of thephysical device, it is important to model these forces of friction. Avery simple model for friction is viscous friction in which thetorque due to friction is proportional to the velocity of jointmotion [12]. Thus s friction ¼ v _ h ð 11 Þ where v is a viscous friction constant. Another possible simple modelfor friction, Coulomb Friction, is sometimes used. Coulomb friction isconstant expect for a sign dependence on the joint velocity: s friction ¼ c sgn ð _ h Þ ð 12 Þ where c is Coulomb friction constant. The value of c is often taken atone value when _ h ¼ 0, the static coefficient and at a lower value, thedynamic coefficient, when _ h a 0. Whether a joint of a particularmanipulator exhibits viscous or Coulomb friction are a complicatedissue oflubricationand othereffects. Areasonable model isto includeboth, since both effects are likely: s friction ¼ c sgn ð _ h Þþ v _ h ð 13 Þ It turns out that in many manipulator joints, friction alsodisplays a dependence on the joint position. A major cause of thiseffect might be gears which are not perfectly round (theireccentricity would cause friction to change according to jointposition). So a fairly complex friction model would have the form s friction ¼ f ð h ; _ h Þ ð 14 Þ These friction models are then added to the other dynamicterms derived from the rigid body model, yielding the morecomplete model s n ¼ M n ð H Þ € H þ V n ð H ; _ H Þþ G n ð H Þþ F n ð H ; _ H Þ ð 15 Þ 2.1. Structure of the robot controller Robot control process is the only process directly influencingthe manipulator. It main task is to compute the set values for thefive servo controllers. Currently the only influence on thedynamics of the system can be exerted by shaping the set valuesto the axis servo controllers. The set values can be computed froma prescribed trajectory expressed in Cartesian space, joint space orin motor increment space. In the case of Cartesian-Euler space,axially-symmetric tools are assumed, as the robot has only fiveDOF. The trajectories can also be computed from or modifiedaccording to virtual sensor readings. The experimental setup isdepicted in Fig. 3.The hardware of the system consists of a 32-bit Intel P-Dmicroprocessor-based computer and five 8-bit Intel 8080 microprocessors. Each of the 8-bit microprocessor-based servo-drivesMA-70 controls a DC electric motor actuating one of the five DOFmanipulator axes (see Fig. 4). The P4 processor is interfaceddirectly to the servo-drives. It transmits position increments toeach one at them and receives feedback signals from them. The P4 Table 1 Standard specifications and dynamic parameters of the robot manipulator. Item Unit Specifications Degree of freedom 5Installation posture On floorStructure Vertical, multiple-joint typeDrive system AC servo motorPosition detectionmethodAbsolute encoderArm lengthShoulder shift mm 0Upper arm 250Fore arm 160Elbow shift 0Wrist length 72Operating range J1 Degree 300( 150 to +150) J2 180( 60 to +120) J3 230( 110 to +120) J4 180( 90 to +90) J5 400( 200 to +200)Speed of motion J1 Degree/s180 J2 90 J3 135 J4 180 J5 210Maximum resultantvelocitymm/s 2100LoadMaximum kg 2Rating 1.5Pose repeatability mm 7 0.02Ambienttemperature 1 C 0–40Mass kg 17Allowable momentload J4 N m 2.16 J5 1.10Allowable inertia J4 kg m 2 3.24 10 –2 J5 8.43 10 –3 Arm reachableradiusmm 410Tool wiring Four input signals, four output signals,motorized hand outputTool pneumaticpipesØ4 3Supply pressure MPa 0.5 7 10% Conveyor System NN Analyzer Robot Manipulator MicrophoneIntelligent Data Acquisition Card Personal Computer Fig. 3. The setup used for the experiments and a schematic diagram. S. Yildirim, I Eski / Robotics and Computer-Integrated Manufacturing 26 (2010) 282–290 285 ARTICLE IN PRESS processors bus is connected by a 16-bit parallel 800 kbaundinterface to the five servo motor controllers and I/O board 2A-RZ365/2A-RZ375. The controller hardware structure of the systemis shown in Fig. 5. 3. Neural networks Neural networks (NN) are made up of simple, highlyinterconnected processing units called neurons each of whichperforms two functions: aggregation of its inputs from otherneurons or the external environment and generation of an outputfrom aggregated inputs [13]. NN can be classified into two maincategories based on their connection structures: feedforward andrecurrent networks. Feedforward networks are the most com-monly used type, mainly because of difficulty of training recurrentnetworks, although the last mentioned are more suitable forrepresenting dynamical systems [14,15].In this experimental investigation, feedforward neuralnetwork type is used to noise analyze in a robot manipulator. Fig. 4. Wiring and piping system diagram for the solenoid valve installation of control system. S. Yildirim, I Eski / Robotics and Computer-Integrated Manufacturing 26 (2010) 282–290 286
