Industrial Robotics Theory Modelling and Control Part 16 ppsx

Friction compensation in hybrid force/velocity control for contour tracking tasks 891 a) b) Figure 13. Tangential velocity signals with no friction compensation and with SFC and AFC for the disk in the A position. a) implicit control; b) explicit control. The mean value of the normal force and tangent velocity RMS error for the dif- ferent experiments is then reported in Table 1. From the results presented it can be deduced that a friction compensation strategy is indeed necessary especially for the explicit control law. This is mo- tivated by the fact that the inner joint position control loops in the implicit con- trol law are somehow able to cope with the friction effects. However, it has to be noted again that the implicit control law requires a greater tuning effort than the explicit one (although, from another point of view, it has the advan- tage that it can be applied to a pre-existing motion control architecture). The Adaptive Friction Compensation strategy provides definitely the best re- sults for the explicit control scheme both in terms of normal force and tangen- tial velocity, while for the implicit control law the performance obtained by the Adaptive Friction Compensation scheme and by the Static Friction Compensa- tion scheme are similar. In any case, the great advantage for the AFC of being a model-free scheme (i.e., no preliminary experiment is required to derive a fric- tion model and robustness to variation of the friction parameters is assured) makes it more appealing to be applied in a practical context. It is worth stressing that the AFC strategy is effective in reducing the normal force and tangential velocity errors especially when the joint velocity sign changes. This fact can be evaluated by considering the resulting two joint ve- locities that would be necessary in order to achieve the required tangential ve- locity of 10 mm/s (for disk A). They are reported in Figure 14 (compare with Figures 12 and 13, for example at time t=3.9 s when the velocity of the first joint changes its sign it appears that the normal force and tangential velocity errors increase significantly when no friction compensation is applied, espe- cially for the explicit control). 892 Industrial Robotics: Theory, Modelling and Control Further, the explicit hybrid force/velocity controller (with AFC) provides basi- cally the same performance (in terms of both normal force and tangential ve- locity errors) disregarding the different normal force and tangential velocity set-points and the different position of the workpiece in the manipulator workspace. This is indeed a remarkable issue that is due to the higher band- width provided by the explicit control than the implicit one. Normal force [N] Tangential velocity [mm/s] Position A Position B Position A Position B Implicit Explicit Implicit Explicit Implicit Explicit Implicit Explicit AFC 3.74 2.97 4.70 2.83 1.8 0.89 2.5 1.3 SFC 3.65 5.16 4.50 4.80 1.5 2.7 2.1 5.1 no-FC 5.26 12.32 6.27 16.05 2.0 5.5 2.9 8.7 Table 1. Mean value of the normal force and tangent velocity RMS error for the different ex- periments Figure 14. Required joint velocities for tracking disk A with the tangential velocity of 10 mm/s Friction compensation in hybrid force/velocity control for contour tracking tasks 893 6. Conclusions Tasks based on force control are seldom performed by robot manipulators in industrial settings. This might be due to the lack of a thorough characterisation of the methodologies developed theoretically from an industrial point of view. Indeed, it has to be demonstrated that a proposed control strategy can be ap- plied effectively in all the possible situations that might arise in an industrial context and, in general, the cost/benefit ratio should be clearly outlined. In this chapter the use of hybrid force/velocity control for the contour tracking of an object of unknown shape performed by an industrial robot SCARA ma- nipulator has been discussed. In particular, both the implicit and explicit con- trol laws have been considered and the compensation of the joint friction effect has been addressed. The pros and cons of the use of an inner joint position control loop have been outlined and it has been shown that the application of a friction compensation strategy is essential if the explicit control law is selected. In this context, the use of the devised Adaptive Friction Compensation strategy is advisable as it pro- vides basically the same (high) performance in the different considered task and its application does not require any previous knowledge of the friction model, that is, no ad hoc experiments have to be performed. 8. References Ahmad, S. & Lee C. N. (1990). Shape recovery from robot contour-tracking with force feedback, Proceedings of IEEE International Conference on Robot- ics and Automation, pp. 447-452, Cincinnati (OH), May 1990 Bona, B.; Indri, M. & Smaldone N. (2003). Nonlinear friction estimation for digital control of direct-drive manipulators. Proceedings of European Con- trol Conference, Cambridge (UK), September 2003 Craig, J. J. (1989). Introduction to Robotics: Mechanics and Control, Prentice-Hall, 0131236296 Daemi M. & Heimann B. (1996). Identification and compensation of gear fric- tion for modelling of robots. Proceedings of CISM-IFToMM Symposium on Theory and Practice of Robots and Manipulators, pp. 89-99, Udine (I) De Schutter J. (1986). Compliant robot motion: task formulation and control. PhD thesis, Katholieke Universiteit Leuven Ferretti, G.; Magnani, G. & Rocco, P. (2000). Triangular force/position control with application to robotic deburring. Machine Intelligence and Robotic Control, pp. 83-91 Haykin, S. (1999). Neural Networks – A Comprehensive Foundation, Prentice-Hall, 0132733501 Indri, M.; Calafiore, G.; Legnani, G.; Jatta, F. & Visioli, A. (2002). Optimized 894 Industrial Robotics: Theory, Modelling and Control dynamic calibration of a SCARA robot. Preprints of 15 th IFAC World Con- gress on Automatic Control, Barcelona (E), July 2002 Jatta, F.; Legnani, G.; Visioli, A. & Ziliani, G. (2006). On the use of velocity feedback in hybrid force/velocity control of industrial manipulators. Control Engineering Practice, Vol. 14, pp. 1045-1055. Legnani G.; Adamini R. & Jatta F. (2001). Calibration of a SCARA robot by con- tour tracking of an object of known geometry, Proceedings of International Symposium on Robotics, pp. 510-515, Seoul (ROK), April 2001 Olsson, H.; Åström, K. J.; Canudas de Wit, C.; Gafvert, M. & Lischinsky P. (1998). Friction models and friction compensation. European Journal of Control, Vol. 4, pp. 176-195 Raibert, M. H. & Craig, J. J. (1981). Hybrid position/force control of manipula- tors. ASME Journal of Dynamic Systems, Measurements, and Control, Vol. 102, pp. 126-133 Roy, J. & Whitcomb, L. L. (2002). Adaptive force control of position/velocity controlled robots: theory and experiments. IEEE Transactions on Robotics and Automation, Vol. 18, pp. 121-137 Siciliano, B. & Villani, L. (1999). Robot Force Control, Kluwer Academic Pub- lisher, 0792377338 Thomessen, T. & Lien T. K. (2000). Robot control system for safe and rapid programming of grinding applications, Proceedings of International Sym- posium on Robotics, pp. 18-30, Montreal (C), May 2000 Visioli, A. & Legnani, G. (2002). On the trajectory tracking control of industrial SCARA robot manipulators. IEEE Transactions on Industrial Electronics, Vol. 49, pp. 224-232 Visioli, A.; Adamini, R. & Legnani, G. (1999). Adaptive friction compensation for industrial robot control. Proceedings of ASME/IEEE International Con- ference on Advanced Intelligent Mechatronics, pp. 577-582, Como (I), July 1999 Volpe, R. & Khosla, P. (1993). A theoretical and experimental investigation of explicit force control strategies for manipulators. IEEE Transactions on Automatic Control, Vol. 38, pp. 1634-1650 Whitcomb L. L.; Arimoto, S.; Naniwa, T. & Ozaki, F. (1997). Adaptive model- based hybrid control of geometrically constrained robot arms. IEEE Transactions on Robotics and Automation, Vol. 13, pp. 105-116 Ziliani, G.; Legnani, G. & Visioli, A. (2005). A mechatronic design for robotic deburring, Proceedings of IEEE International Symposium on Industrial Elec- tronics, pp. 1575-1580, Dubrovnik (HR), June 2005 Ziliani, G.; Visioli, A. & Legnani, G. (2006). Gain scheduling for hybrid force/velocity control in contour tracking task. International Journal of Advanced Robotic Systems Vol. 3, pp. 367-374. 895 33 Industrial Robot Control System Parametric Design on the Base of Methods for Uncertain Systems Robustness Alla A. Nesenchuk and Victor A. Nesenchuk 1. Introduction Industrial robots often operate in conditions of their parameters substantial variation that causes variation of their control systems characteristic equations coefficients values, thus generating the equations families. Analysis of the dy- namic systems characteristic polynomial families stability, the stable polyno- mials and polynomial families synthesis represent complicated and important task (Polyak, 2002, a). Within the parametric approach to the problem the se- ries of the effective methods for analysis have been developed (Bhattaharyya et al., 1995; Polyak, 2002, a). In this way, V. L. Kharitonov (Kharitonov, 1978) proved that for the interval uncertain polynomials family asymptotic stability verification it is necessary and enough to verify only four polynomials of the family with the definite constant coefficients. In the works of Y. Z. Tsypkin and B. T. Polyak the frequency approach to the polynomially described systems robustness was offered (Polyak & Tsypkin, 1990; Polyak & Scherbakov, 2002; Tsypkin & Polyak, 1990; Tsypkin, 1995). This approach comprises the robust stability criteria for linear continuous systems, the methods for calculating the maximal disturbance swing for the nominal stable system on the base of the Tsypkin – Polyak hodograph. These results were generalized to the linear dis- crete systems (Tsypkin & Polyak, 1990). The robust stability criterion for the re- lay control systems with the interval linear part was obtained (Tsypkin, 1995). The super-stable linear systems were considered (Polyak & Scherbakov, 2002). The problem for calculating the polynomial instability radius on the base of the frequency approach is investigated (Kraev & Fursov, 2004). The technique for composing the stability domain in the space of a single parameter or two parameters of the system with the D-decomposition approach application is developed (Gryazina & Polyak. 2006). The method for definition of the nominal polynomial coefficients deviations limit values, ensuring the hurwitz stability, has been offered (Barmish, 1984). The task here is reduced to the single-parameter optimization problem. The similar tasks are solved by A. Bartlett (Bartlett et al., 1987) and C. Soh (Soh et 896 Industrial Robotics: Theory, Modelling and Control al., 1985). Conditions for the generalized stability of polynomials with the line- arly dependent coefficients (polytopes) have been obtained (Bartlett et al., 1987; Rantzer, 1992). One of the most important stages, while calculating dynamic systems with un- certain parameters, is ensuring robust quality. The control process qualitative characteristics are defined by the characteristic equations roots location in the complex plane (the plane of system fundamental frequencies). In this connec- tion, three main groups of tasks being solved can be distinguished: determin- ing the assured roots location domain (region) for the given system, finding conditions of whether roots get into the given region or not (determination of the Λ-stability conditions) and locating roots in the given domain (ensuring Λ- stability). The frequency stability criteria for the linear systems families and also the method for finding the largest disturbance range of their characteristic equa- tions coefficients, which guarantees the system asymptotic stability, are con- sidered by B. T. Polyak and Y. Z. Tsypkin (Polyak & Tsypkin, 1990). The as- sured domain of the interval polynomial roots location is found in (Soh et al., 1985). The root locus theory is used in (Gaivoronsky, 2006) for this task solu- tion. Conditions (Vicino, 1989; Shaw & Jayasuriya, 1993) for the interval poly- nomial roots getting into the given domain of some convex shape are defined. The parametric approach to robustness, based on the root locus theory (Rim- sky, 1972; Rimsky & Taborovetz, 1978; Nesenchuk, 2002; Nesenchuk, 2005), is considered in this chapter in application to the industrial anthropomorphous robot control system parametric design. The developed techniques allow to set up the values of the parameter variation intervals limits for the cases when the stability verification showed, that the given system was unstable, and to en- sure the system robust quality by locating the characteristic equations family roots within the given quality domain. 2. Industrial robot and its control system description Most industrial robots are used for transportation of various items (parts), e. g. for installing parts and machine tools in the cutting machines adjustments, for moving parts and units, etc. During the robot operation due to some internal or external reasons its parameters vary, causing variation of the system charac- teristic equation coefficients. This variation can be rather substantial. In such conditions the system is considered, as the uncertain system. 2.1 General description of the anthropomorphous industrial robot The industrial robot considered here is used for operation as an integrated part of the flexible industrial modules including those for stamping, mechanical as- Industrial robot control system parametric design on the base of methods for uncertain… 897 sembly, welding, machine cutting, casting production, etc. The industrial robot is shown in fig. 1. It comprises manipulator 1 of anthropomorphous structure, control block 2 including periphery equipment and connecting cables 3. Ma- nipulator has six units (1–8 in fig. 1) and correspondingly is of six degrees of freedom (see fig. 1): column 4 turn, shoulder 5 swing, arm 6 swing, hand 7 swing, turn and rotation. The arm is connected with the joining element 8. Controlling robots of such a type, belonging to the third generation, is based on the hierarchical principle and features the distributed data processing. It is based on application of special control processors for autonomous control by every degree of freedom (lower executive control level) and central processor coordinating their operation (higher tactical control level). 2.2 Industrial robot manipulator unit control system, its structure and mathematical model Executive control of every manipulator unit is usually executed in coordinates of this unit (Nof, 1989) and is of the positional type. It is the closed-loop servo- control system not depending on the other control levels. Although real unit control is executed by a digital device (microprocessor, controller) in a discrete way, the effect of digitization is usually neglected, as the digitization fre- quency is high enough to consider the unit and the controller as the analog (continuous) systems. As for the structure, the unit control loops are almost similar and differ only in the parameter values. Therefore, any unit of the in- dustrial robot can be considered for investigating the dynamic properties. Figure 1. Anthropomorphous industrial robot 898 Industrial Robotics: Theory, Modelling and Control The structure of the manipulator unit subordinate control is shown in fig. 2. The simplified version of the structure is presented in fig 3. In fig. 2 the plant is represented by elements 1–4 (a DC motor); 5 is the sensor transforming the analog speed signal into the speed code (photo-pulse sensor), 6 is the element combining the speed PI regulator, code-pulse width trans- former and capacity amplifier, 7 is the transformer of analog position signal into the position code (photo-pulse sensor), 8 is the proportional regulator of the manipulator shoulder position, 9 is the transfer mechanism (reducer). In fig. 3 the transfer function ssWsW pp )()( ' = where )(sW p is the plant transfer function. Substitute corresponding parameters and express the plant transfer function as follows: sCs C R jjs C L jj U sW e Ɇ A lm Ɇ A lm g p ++++ = ϕ = 23 )()( 1 )( , (1) where g U is the input voltage, ϕ is the object shaft angle of rotation. Figure 2. Control system for the industrial robot manipulator shoulder unit On the basis of (1) write the manipulator unit control system characteristic equation Industrial robot control system parametric design on the base of methods for uncertain… 899 0 2 1 234 =++++ TLj KKKC s TLj KKC s Lj CC s L R s Am spM Am sɆ Am Ɇe A A or as 0 43 2 2 3 1 4 0 =++++ asasasasa , (2) where 1 0 =a ; A A L R a = 1 ; Al’m Me Ljj CC a )( 2 + = ; TLjj KKC a Alm sɆ )( 1 3 + = ; TLjj KKKC a Alm spM )( 2 4 + = ; - A R is the motor anchor resistance; - A L is the anchor inductance; - l j is the load inertia moment; - m j is the anchor inertia moment; - e C is the electric-mechanical ratio of the motor; - M C is the constructive constant of the motor; - T is the time constant of the PI regulator; - 1 K and 2 K are photo-electric sensor coefficients; - s K and p K are gains of regulators by speed and position correspon- dingly. Suppose the robot unit has the following nominal parameters: - A R = 0,63 Ω; - A L = 0,0014 henry; - l j = 2,04⋅ 52 10 k g /m − - m j = 40,8⋅ 52 10 k g /m − ; - e C = 0,16 rad sV ⋅ ; - M C = e C ; - T= 0,23 s; - 1 K = 66,7, 2 K = 250; - .5,2,078,0 == ps KK 900 Industrial Robotics: Theory, Modelling and Control Figure 3. Structure of the position control system loop for the manipulator shoulder unit After substitution of the nominal values into (2) rewrite the unit characteristic equation as 01056,0106,010427,0105,0 8725334 =⋅+⋅+⋅+⋅+ ssss (3) The coefficients of (3) are the nominal ones and while robot operation they of- ten vary within the enough wide intervals. For this reason when calculating the robot control system it is necessary to consider the parameters uncertainty and ensure the control system robustness. 3. The techniques for robust stability of systems with parametric uncertainty The method is described for synthesis of the interval dynamic system (IDS) stable characteristic polynomials family from the given unstable one, based on the system model in the form of the free root locus portrait. This method al- lows to set up the given interval polynomial for ensuring its stability in cases, when it was found, that this polynomial was unstable. The distance, measured along the root locus portrait trajectories, is defined as the setting up criterion, in particular, the new polynomial can be selected as the nearest to the given one with consideration of the system quality requirements. The synthesis is carried on by calculating new boundaries of the polynomial constant term variation interval (stability interval), that allows to ensure stability without the system root locus portrait configuration modification 3.1 The task description While investigating uncertain control systems for getting more complete rep- resentation of the processes, which occur in them, it seems substantial to dis- cover correlation between algebraic, frequency and root locus methods of in- [...]... equation 924 Industrial Robotics: Theory, Modelling and Control 6 Conclusion Industrial robots represent devices, which usually operate in conditions of substantial uncertainty Therefore, in this chapter the problem of uncertain control systems stability and quality is considered in application to the industrial robot analysis and synthesis tasks solution The task for synthesis of the interval control systems... Kharitonov’s polynomials and is equal to na = n – m = 4 – 0 = 4, where m is the number of poles for function (5) 910 Industrial Robotics: Theory, Modelling and Control The centers of asymptotes are located on the axis σ and have coordinates: σ h1 = 2,10; σ h 2 = 2,90; σ h 3 = 2,10; σ h 4 = 2,90 (see fig 4) The asymptotes centers coordinates coincide in pairs: for the pair h1 ( s ) and h3 ( s ) , and also for... (2002), a Robust Stability and Control [in Russian], Nauka, ISBN 5-02-002561-5, Moscow 926 Industrial Robotics: Theory, Modelling and Control Polyak, B & Scherbakov, P (2002), b Superstable linear control systems I, II ([n Russian] Avtomatika i Telemekhanika, No 8, (2002) 37–53, ISSN 005-2310 Rantzer, A (1992) Stability conditions for polytopes of polynomials IEEE Trans Automat Control, Vol 37, N 1,... degree of stability and constant damping For solving the task, apply the root locus fields of the circular image (circular root locus fields – CRLF) (Rimsky, 1972; Nesenchuk, 2005) The field function (19) and the level lines equation (20) for the CRLF in the general form: f* = f*(σ, ω, a, b) (22) 914 Industrial Robotics: Theory, Modelling and Control f*(σ, ω, a, b) = ρ2 (23) where a and b are the image... line, inscribed into the quality domain, the following systems of equations (25), (26) and (29) were solved: 920 Industrial Robotics: Theory, Modelling and Control 6ω 4 + 12ω 2 σ 2 + 60ω 2 σ + 82,8ω 2 + 6σ 4 + 60σ 3 + 226σ 2 + 316 + 90,6 = 0 ; σ = −1,28 6ω 4 + 12ω 2 σ 2 + 60ω 2 σ + 82,8ω 2 + 6σ 4 + 60σ 3 + 226σ 2 + 316 + 90,6 = 0 σ = −4,68 ; (6ω 4 σ + 15ω 4 + 12ω 2 σ 3 + 90ω 2 σ 2 + 226ω 2 σ + 158ω... *(σ,ω) (19) 912 Industrial Robotics: Theory, Modelling and Control and the root locus field level lines equation f *(σ,ω) = L, (20) where L = const = tj, tj is the parameter of the j-th image, – ∞ ≤ tj ≤ + ∞, j = 1, 2, 3, … 4.1 The task formulation Define the quality domain Q (fig 5) in the left complex half-plane of the system fundamental frequencies (roots plane), bounding the equation (16) roots location... 4 + a1 s 3 + a 2 s 2 + a 3 s ) ψ(s) The control system characteristic equation is (32) 922 Industrial Robotics: Theory, Modelling and Control φ( s ) + a 4 ψ ( s ) = s 4 + a1 s 3 + a 2 s 2 + a 3 s + a 4 = 0 (33) The limit values of equation (33) coefficients variation intervals are entered to the input of the package ANALRL for computer-aided investigation of control systems with variable parameters... polynomials are completely located in the left half-plane, the given interval system is asymptotically stable (Kharitonov, 1978) 904 Industrial Robotics: Theory, Modelling and Control Figure 4 Root loci of the Kharitonov's polynomials for the system of class [4;0] Industrial robot control system parametric design on the base of methods for uncertain… 905 3.3 Investigation of the characteristic polynomial... the variable parameter plane k 915 916 Industrial Robotics: Theory, Modelling and Control In the first case the circular image center will be located in point C, where k = 0 (fig 6, ) In the second case the field localization centers should be located on the TERL positive branches segments being completely located within the given quality domain Coordinates u = a and υ = b (fig 7, ) of the corresponding... locus relative to the coefficient ak 902 Definition 5 Definition 6 Remark 1 Remark 2 Industrial Robotics: Theory, Modelling and Control The root locus relative to the dynamic system characteristic equation constant term name as the free root locus of the dynamic system The points, where the root locus branches begin and the root locus parameter is equal to zero, name as the root locus initial points . is applied, espe- cially for the explicit control) . 892 Industrial Robotics: Theory, Modelling and Control Further, the explicit hybrid force/velocity controller (with AFC) provides basi- cally. properties. Figure 1. Anthropomorphous industrial robot 898 Industrial Robotics: Theory, Modelling and Control The structure of the manipulator unit subordinate control is shown in fig. 2. The simplified. = 0 ,16 rad sV ⋅ ; - M C = e C ; - T= 0,23 s; - 1 K = 66,7, 2 K = 250; - .5,2,078,0 == ps KK 900 Industrial Robotics: Theory, Modelling and Control Figure 3. Structure of the position control