Feeback Error Learning Neural Network Applie to a Scara Robot Fernano Passol Dept. of Electrical Engineering University of Passo Funo Passo Funo, Brazil passol@upf.tche.br Abstract This paper escribes experimental results applying artificial neural networks to perform the position control of a real scara manipulator robot. The general control strategy consists of a neural controller that operates in parallel with a conventional controller base on the feeback error learning architecture. The main avantage of this architecture is that it oes not reuire any moification of the previous conventional controller algorithm. MLP an RBF neural networks traine online have been use, without reuiring any previous knowlege about the system to be controlle. The approach has performe very successfully, with better results obtaine with the RBF networks when compare to PID an sliing moe positional controllers. Marcelo Ricaro Stemmer Dept. of Automation System Feeral University of Santa Catarina Florianópolis, Brazil marcelo@as.ufsc.br The main purpose was to evaluate new algorithms for position/force control, since the robot is also euippe with a force sensor. Fig. shows the INTER scara robot. Introuction This paper escribes an iscusses practical results obtaine with the use of computational intelligence techniues, specifically artificial neural networks, applie to the position control of a real manipulator robot. The neural controller propose in this work was applie in a real scara robot installe at the Inustrial Automation Laboratory of the Feeral University of Santa Catarina, Brazil. The work is the result of a cooperation between the Automation an Mechanical Engineering epartments. The robot was manufacture by the Institute of Robotics (IfR) of the ETH (Swiss Feeral Institute of Technology, http://www.ifr.mavt.ethz.ch/). Differently from most inustrial manipulator robots, this one has an open architecture, which allows the implementation of any type of control law. The man-machine interface is accomplishe through the XO/2 Real-Time Operational System or Oberon System 3 for Winows (http://www.oberon.ethz.ch/) also evelope in the ETH especially for the mecatronics area. This real-time operational system also incorporates an object oriente programming language which coul be seen as a successor of Moula2 an Pascal. Figure. INTER scara robot. Manipulator robots are a type of non-linear an time variant systems. Conventional controllers, such as PD an PID, are use among other avance an robust controllers that reuire some knowlege about the ynamic moel of the system uner control. In the case of manipulator robots, it is ifficult to obtain some parameters, as the inertia matrix an mass centers of any joint, with sufficient accuracy. Therefore either aaptive controller are reuire to overcome these inaccurate parameters or control laws base on Lyapunov functions are evelope to guarantee some kin of stability [4]. Both approaches reuire some knowlege about the system. This work explores a computational intelligence techniue, namely artificial neural networks, to eal with this situation. In particular, control algorithms base on neural networks an fuzzy logic techniues are consiere intelligent control approaches that o not reuire any previous knowlege about the system to be controlle. The main goal of this work was to explore an
effective computational intelligence techniue to control this complex system using a structure as simples as possible, with preference to one which reuires less change in the previous conventional controller alreay installe in the system, o not overloa the main processor an is robust against isturbance an loa effect variations. 2 Neural Controller Types Artificial Neural Networks (As) have been applie to several cases of control systems, showing special aeuacy when we have to eal with complexity, nonlinearity or uncertainty [3]. The neural approach is interesting, notably in the cases where: a) Mathematical moels of the process are poor or o not even exist an linear moels are inaeuate to represent the system with sufficient accuracy; b) The system works satisfactorily with an existing controller but its performance eteriorates substantially when high performances (e.g. spees) are reuire, so non-linear controllers become necessary. As have prove their ability to approximate arbitrary nonlinear maps an the availability of methos for ajusting their parameters on basis of input an output ata makes them particularly attractive in ientifiers an controllers [3]. Narenra [3] also comments that it seems to be valuable to keep linear an non-linear components working in parallel, where the neural networks represent the non-linear components. He also mentions the brief learning time perios an the increase of accuracy that results from this kin of integration. In the control systems area, a few neural moels have been prove to be more suitable than others, namely the: ) Multilayer Perceptron networks (MLP); 2) Raial Base Function networks (RBF). Among several ways to apply As in a control scheme, we can cite: (i) inverse ientification (reuires unesirable off-line training), (ii) reference moel structure, (iii) internal moel control, (iv) preictive control (uses two As, one of them traine off-line to ientify the system), (v) optimal control (also reuires two nets: the first one to uantify the state space of the system an the next acts as a classifier). Articles [7] an [2] iscuss two learning architectures that seem to be the most appropriate an promising: a) Feeback-error learning architecture; an b) Aaptive learning architecture. The feeback error learning approach is characterize by the A inserte in the feeback path to capture the nonlinear characteristics of the system. The A weights are tune on-line with no off-line learning phase an, when compare with the aaptive techniue, we o not reuire any knowlege of the robot ynamics, linearity in the unknown system parameters or the teious computation of a regression matrix. Thus, this approach is moel-free an represents an improvement over aaptive techniues []. 2. Multilayer Perceptron Net This network consists of a set of sensory input units (source noes) that constitute the input layer, one or more hien layers an an output layer. The input signal propagates through the network in a forwar irection, on a layer-by-layer basis [6]. Multilayer perceptrons coul be traine in a supervise manner using the back-propagation algorithm. Backpropagation is base on the error-correction learning rule an uses a least-mean-suare error algorithm to ajust its connection weights. The error back-propagation learning consists of two stages: first, a forwar phase, when the input vector is applie to the sensory noes of the network, an its effect propagates through the network layer by layer. ly, an output set is prouce as the current response of the network. During the forwar phase the weights of the network are kept unchange. In the secon phase, the backwar phase, an error signal is propagate backwar through the network against the irection of synaptic connections an the weights are ajuste to make the current response of the network move closer to the esire response base on a steepest escent algorithm, or back propagation weight upate rule, also calle generalize elta-rule [6]. 2.2 Raial Base Functions Net The basic structure of the RBF network consists of three layers. Different from the MLP networks, the layers here have ifferent tasks. The first layer is passive an only connects the moel to the real worl. The secon layer is a uniue hien layer. It performs a non-linear transformation from the input vector space to the internal vector space. The last layer is the output layer an transforms internal vector space into output vector space in a linear manner. There are several algorithms available to train the network [6][3][5]. These two types of neural nets can be universal function approximators [6][5]. 3 Controller Propose The controller propose here uses a conventional PD or PID that performs in parallel with an artificial neural network traine on-line. This kin of architecture for neural controllers is known as feeback error learning
because the net uses the output signal generate by the conventional controller as its own error signal that is back propagate for learning purposes [3][]. Fig. 2 shows the architecture applie in this case. Path Generator, &, &&, & - & & Neural Net τ Conventional Controller τ Figure 2. Controller architecture. Robot Both types of A teste perform with the same input ata vector: x = [ & & ], where is the vector of current joint positions; & is the vector of current joint spees (obtaine through numerical ifferentiation); & & correspons to the esire joint accelerations (like in other manipulators, there is no accelerometer available for each joint, so the esire acceleration compute by the path generator was use). These inputs were boune into its maximum an minimum possible operational values for this robot an then scale between the neural input range -.9 to.9 only for the MLP nets. Note that, ifferent from MLP nets, the RBF nets o not nee a scale proceure as they coul eal irectly with rough ata, but it was necessary to organize the input ata into three ifferent classes: ) joint positions, 2) joint spees an 3) joint accelerations see fig. 3. The iea behin organizing the ata into ifferent classes comes from earliest experience with fuzzy inference systems. One coul compare RBF networks with fuzzy inference systems [2]. Each class of input ata coul be unerstoo as linguistic operations of fuzzy systems. Each class of ata is mappe using m Gaussian functions an coul be compare to the m membership functions that will be use in a fuzzy system. An finally, the rules an the way they are evaluate in a fuzzy system were performe by the output layer of a RBF network. Each synaptic connection of the output layer coul be compare to the fuzzy IF-THEN-rules. The overall outputs are erive through the weighte sum one by the output layer [9]. Hence, m Gaussian functions were create to categorize each vector of each class of input ata, as can be seen in fig. 3. One coul argument the massive amount of ata reuire for the input layer (3 classes 4.o.f. m Gaussian functions) is a rawback of this approach, but this solution was relate to the final application in min in this case. Motions in the plane XY were one by the first two joints of the robot. Height (Z), & an final orientation (θ) is performe by the last two joints of this robot but there is a mechanical coupling between them, i.e., changes only in the final orientation of the robot result in a small change for the final height reache by the robot. That represents an extra challenge to evelop an effective controller to this kin of robot. Input Layer & & & & & 2 3 & & 2 & & 2 & 3 & & 3 Green Functions ϕ N- ϕ m ϕ m i ϕ m ϕ m Hien Layer w ij Σ Σ Σ 2 Σ 3 Figure 3. Structure of the RBF A use. Outputs τ τ τ 2 τ 3 The centers x i of the m esire Gaussian functions are fixe, base on the range (minimal an maximal values) of the input vector. That allows to efine the maximum Eucliian istance, max, between each Gaussian centers as: max =(x max -x min )/(m-) an then to fix the stanar eviation (or sprea) of each Gaussian function to be use accoring to: max σ = 2 m The traitional back-propagation algorithm expane with momentum term was use to ajust in real-time the weights of the MLP an RBF networks [6]. The aition of the momentum term to the elta rule traitionally use to upate the weights of the net (base on the metho of ()
the escening graient of the error signal), spees up this algorithm, it eliminates ecurrent oscillations of the calculation of the graient an prevents the net to get paralyze into a point of minimum local (an not global) in its surface errors [6]. Both networks en with 4 neurons, each one to evaluate the torue neee to comman each joint motor of the robot. The final torue sent to each joint is efine as: τ τ τ = (2) where τ is relate to the torue evaluate by the conventional feeback controller that performs in parallel with one of these networks. PD an PID controllers working in the joint space have been use. The euation for the PID use is given by: τ B ( K ~ K ~ K &~ = ( ) p i t ) (3) where B() refers to the inertia matrix of the robot (estimate); ~ = ( ) represents the error between the esire an the actual joint position; &~ refers to the velocity error; K p is the vector of proportional gains for each joint; K i refers to the integral vector gains an K is the erivative gain vector for each joint. To get a PD action over the system, the K i vector was not use (eual to zero). Table shows the parameters use for the teste PD/PID controllers. Table. PID parameters use. Joint Joint Joint 2 Joint 3 Kp 49 2 9 44 K 4 22 6 24 Ki 478 2 92 4 3 Experimental Results The algorithms relate with this neural controller ha been implemente in the form of a real-time task that runs with a sampling rate of millisecon. At each millisecon is evaluate the action of conventional controller, evaluate the forwar phase of the neural net an still the backwar phase while the trajectory error, ~ >. (ra m). The controller was teste over the trajectory shown by fig. 4. Table 2 shows the joint positions, spees an accelerations evelope for each joint. All the four joints were move simultaneously. Fig. 5 shows the output torues evelope by ifferent controllers for the joint 3 (the last an faster). Note the ifferent performances evelope by the PDMLPc (MLP with one single hien layer), PDMLP2c (MLP with two hien layers), PDRBF(5) (RBF with 5 Gaussina functions) an PIDRBF controllers teste. Figure 6 shows the trajectory error over time. During the initial one-thir of the robot configuration change perio the As are in their learning time an the conventional controller still preominates in the joint control. But even before the en of this perio of time, it coul be seen that the As output torue takes preominance over the final torue evaluate (fig. 6). It coul be seen that the A learns the ynamic behavior of the system an then oes the ynamic compensation that results in higher performance compare to a conventional controller. Y [cm] 6 5 4 3 2 - Superior View [XYθ] b a -2-2 X [cm] Z [cm] 4 35 3 25 2 b Lateral View [XZ] a 2 X [cm] Figure 4. Trajectory use for test of table. Table 2. Data of trajectory execute. Data Joint Joint Joint 2 Joint 3 a 2.445 -.85 25.47 -.57 (ra) (ra) (cm) (ra) b 49.7 46.6. (ra) (ra) (cm) (ra) & max & & max -.7 (ra/s).85 (ra/s 2 ).9 (ra/s). (ra/s 2 ) 22.9 (cm/s) 47.4 (cm/s 2 ).85 (ra/s) -.93 (ra/s 2 ) The best results for the MLP nets were achieve with learning rate η =.35 an momentum term α=.5. Relate to the RBF nets, the best learning parameters foune were: η =.5 an α =.5. Note that a PID performing with a RBF net allows the better performance (fig. 5() an 5(e)) followe by the PDRBF, PDMLP an finally the single PD. It was note that the use of two hien layers for the MLP A oes not imply in a better performance an moreover as a small resiual memory effect in presence of a isturbance on the system (this behavior has been observe in tests where an elastic string was place in the mile of a linear trajectory).
Torues Joint 3 Torues Joint 3.4.8.6.4.8.4.6 τ.2 -.2 -.4.4.2 τ -.6 2 3 4 5 6 (a) PD controller. -.2 3 4 5 6 7 () PDRBF(5). Torues Joint 3 Torues Joint 3.4.8.6.4.2 -.2 -.4 τ 2 3 4 5 6 (b) PD MLPc. Torues Joint 3 τ.4.8.6.4.2 -.2 -.4 -.6 τ τ 2 3 4 5 6 (e) PID RBF(5). Figure 5 (cont). Output torue evelope for joint 3.4.8.6.4.2 τ τ x -3 5 PD PDMLP2c PDRBF PIDRBF Joint 3 Error Position PD PDRBF -.2 -.4 -.6 3 4 5 6 7 (c) PD MLP2c. (ra) 5 PIDRBF Figure 5. Output torue evelope for joint 3. -5 PDMLP2c 3 4 5 6 7 8 9 Sampling time (k) Figure 6. Joint 3 tracking error.
Experimental results have also emonstrate that the aition of more than 5 Gaussian functions in the RBF A controller slightly increases the performance but at the expenses of a significant higher computational cost. 4 Conclusions This paper has presente a practical an successful application of a neural controller performing in parallel with a conventional controller in the position an trajectory following control of a real robot. The use of a conventional controller performing in parallel with the As is avantageous to maintain the robustness of the system when the A become saturate (ue to high learning rates) an is important to force the reajustment of the synaptic weights of the A use when the robot changes its configuration. As soon as the A captures the ynamic behavior of the system, the final torue is given uite totally by the A an a higher performance coul be achieve. Both the MLP an RBF A perform very well, but RBF oes it better an faster than a MLP, mainly if it works in parallel with a PID controller. An aitional an unexpecte avantage coul be achieve with the PIDRBF controller: robot motion with lowest noise levels (uite silent). On the other han, there is also a rawback: A reuires more processing power to work in parallel with the conventional controller see table 3. Table 3. Power computer resources reuire. Controller Processing tme Type Min Max PD 4 4 PDMLP2c 94 385 PDRBF(5) 333 579 PDRBF(7) 425 679 Note: values expresse in nanosecons. Even if computer resources are short, a simple PDMLP with one hien layer allow better results than a PD controller. Otherwise, if higher processing power is available, a PIDRBF achieves the best results. Since the neural controllers propose here have performe very successfully, future irections of this works inten to establish an integrate position/force control over a hybri control architecture to eal with robot applications that imply some contact with the environment. References [2] Fritzke, B; Incremental neuro-fuzzy systems, Applications of soft computing, SPIE International Symposim on Optical Science, Engineering an Instrumentation, San Diego, 997. [3] Gabrijel I. an Dobnikar, A., Aaptative RBF Neural Network, SOCO'97 Conference, Nimes, France, September, 997, pp. 64 7, URL: http://cherry.fer.uni-lj.si:8/~gabriel/soco97/soco97.zip. [4] Ge, S. S., Hang, C. C. an Woon, L. C., Aaptive neural network control of robot manipulators in task space, IEEE Trans. On Inustrial Electronics, vol. 44, no. 6, 997, pp. 746-752. [5] Girosi, F. an Poggio, T., Networks an the best approximation property, in M. M. Gupta an D. H. Rao (es), Neuro-Control Systems, Theory an Applications, IEEE Pres: Piscataway, NJ, 993., pp. 257-264. [6] Haykin, S., Neural Networks: A Comprehensive Founation, 2 n. E., Prentice Hall: New Jersey, 999. [7] Katic, D. an Vukobratovic, M., Connectionist base robot control: an overview, 3 th IFAC, vol. b-5, 6, San Francisco, 996, pp. 69-74. [8] Keller, R., CSCI 52 neural networks course, Lecture slies, Harvey MU Coolege, Computer Sci. epot., Claremont, CA, 999, URL: http://www.cs.hmc.eu/claremont/keller/52- slies/inex.html. [9] Kiguchi, K. an Fukua, T., Intelligent position/force controller for inustrial robot manipulators applications of fuzzy neural networks, IEEE Trans. On Iustrial Electronics, vol. 44, no. 6, 997, pp. 753-76. [] Kim, Y. H., an Lewis, F. L., Neural network output feeback control of robot manipulators, IEEE Trans. On Robotics an Automation, vol 5, no. 2, 999, pp. 3-39. [] Lightboy, G. an Irwin, G. W., Nonlinear control sstrcutures base on embee neural systems moels, IEEE Trans. On Neural Networks, vol. 8, no. 3, 997, pp. 553-567. [2] Morris, A. S., an Khemanissia, S, Artificial neural networks base intelligent robot ynamic control, in A. M. S. Zalazala an A. S. Morris (es), Neural Networks for Robotic Control - Theory an Applications, chapter 2, Ellis Horwoo: Great Briain, pp. 26-63. [3] Narenra, K. S., Neural networks for real-time control, 36 th IEEE Conference on Decision an Control, San Diego, CA, 997, pp. 26-3. [4] Sciavicco, L. an Siciliano, B., Moeling an Control of Robot Manipulators, McGraw-Hill, 996. [5] Talebi, H. A., Patel, R. V. an Khorasani, K., Ibverse yamics control of flexible-link manipulators using neural networks, IEEE Int. Conf. on Robotics an Automation, Leuven, Belgiun, 998, pp. 86-8. [6] Zalzala, A. M. S., Moel-base aaptive neural structures for robotic control, in A. M. S. Zalzala an A. S. Morris (es), Neural Networks for Robotic Control Theory an Applications, Ellis Horwoo: Great Briatin, 996, chapter 4, pp. 8-5. [7] Zell, A. et all, SS: Stuttgart Neural Network Simulator, User Manual, Version 4., University of Stuttgart, 995, URL: http://www-ra.informatik.unituebingen.e/ss/usermanual/noe.htm. [] Er, M. J., an Liew, K. C., Control of Aept ne Scara robot using neural networks, IEEE Trans. On Inustrial Electronics, vol. 44, no. 6, 997, pp. 762-768.