ScienceDirect. Force-Torque Control Implementation for 2 DoF Manipulator

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1 Available online at ScienceDirect Proceia Engineering 69 ( 2014 ) th DAAAM International Syposiu on Intelligent Manufacturing an Autoation, 2013 Force-Torque Control Ipleentation for 2 DoF Manipulator Victor Titov*, I.Sharyko, Sergey Isaenko Departaent of robotic syste esign Russian State Scientific Center for Robotics an Technical Cybernetics, Saint-Petersburg, Russia Abstract This paper escribes an approach to force control of two egrees of freeo robot anipulator. Aspects of control ipleentation concerning a joint torque sensor are iscusse an a technique to its correction an calibration is presente. Twolevel control schee is use for the purposes of easier ipleentation. Such an approach has prove to be convenient in organizing general control structure an intrinsic to the two-tie-scale ynaics of the syste. For the fast part of syste ynaics (corresponing to controlling the value easure by the torque sensor) joint oel is presente. Base on this oel, two variants of torque control loop are evelope an their ters of application are outline. Two types of control strategies for the slow part of syste ynaics inclue an ipeance control an force/torque control with gravity copensation as well as trajectory tracking base on the ipeance control The Authors. Publishe by Elsevier Lt The Authors. Publishe by Elsevier Lt. Open access uner CC BY-NC-ND license. Selection an peer-review uner responsibility of DAAAM International Vienna. Selection an peer-review uner responsibility of DAAAM International Vienna Keywors: torque sensor; force control; robot anipulator; callibration; zero reaing fluctuation 1. Introuction In the last ecae the worl has witnesse ajor avance in the fiel of force/torque control both practical an theoretical. Though, the first publications an experiental results concerning force/torque control can be ate own to the early 80s (an even earlier), the nuber of publications approaches its axiu fro 2005 to 2009 an eclining after that (accoring to [1-2]). Such a peculiar istribution ay be explaine as the result of recent iproveents in icroelectronics an coputers power that akes it possible to ipleent the theoretical achieveents in harware. As one of such ipleentations worth entioning is the outcoe of DLR Institute of Robotics un Mechatronics har work with their light-weight robots that uses ipeance control fraework [3-4]. Force/torque control consists of two central sub probles: * Corresponing author. Tel.: ; fax: E-ail aress: victortitov2005@ail.ru The Authors. Publishe by Elsevier Lt. Open access uner CC BY-NC-ND license. Selection an peer-review uner responsibility of DAAAM International Vienna oi: /j.proeng

2 Victor Titov et al. / Proceia Engineering 69 ( 2014 ) Data acquisition forces/torques in the wrist or just torques in the joints Control incorporating this ata into the control loop to enhance the overall quality of control The forer inclues sensor esign, calibration, easureent an preliinary ata processing (filtering, correction). The later assues the forulation of the control law that woul use the force/torque ata (along with other feeback) to achieve the expecte robot behavior. In this paper both probles are tackle to hanle the control of 2 egrees of freeo (DoF) robot anipulator as an exaple of such systes. The robot is equippe with ebee torque sensors in each joint. Due to coplex echanical interaction within each joint, acquisition of the torque ata faces a proble of aitive istortion coponents present in the raw reaing of the joint torque. This for the first goal of the paper as a search for the correction of the torque easureent that leas to eliination or reuction of aitive istortions an increase accuracy. The another proble consists of choosing the torque control law for at the joint level that correspons to the upper level control strategies. In the present work two types of well-known upper level control strategies are teste: ipeance control an force/torque control with gravity copensation. The control laws for the joint level have to eet the requireent of sufficient accuracy an transient behavior while saving the easiness of ipleentation an low coputational coplexity as well as be suitable for the upper level control strategies peculiarities. Though in theory a single optial solution ay be preferable, in practice, ue to any factors influencing the control engineering, a universal solution is ifficult to fin. That happens to be true for the syste iscusse in the paper. Thus the secon goal is the forulation of the joint level torque controllers that eet the requireents. In the light of the probles state the paper is organize as follows. First the harware use is briefly escribe an the probles with ata acquisition are outline. Then several techniques of zero biases eliination are iscusse an the optial choice is ae for icrocontroller ipleentation. In the forth section the oel of the flexible joint is presente in orer to give necessary explanations for the control schees in the fifth section. In the fifth section both the ipeance an force/torque with gravity copensation control strategies of the upper control level are also entione. Finally the conclusion an iscussions su up the results an ways for future iproveents. 2. Harware use 2.1. Manipulator The robot use in this work is two DoF planar robot anipulator (see fig. 1(a)). It consists of two echatronic joint an a gripper (substitute for aitional payloa in the figure). Joints are ae priarily of aluiniu an linke with aluiniu tubes in orer to lower its weight. The total weight of the anipulator is 14 kg. Due to universal electrical connectors an echanical conjunctions the anipulator becoes reconfigurable. Each joint can be rotate about the previous links longituinal axis with 45 step Joint The joints are coplete echatronical oules. A torque rive accopanie with a strain wave gearing (with 100 an 160 reuction ratio for elbow an shouler respectively ) are ebee into an aluinu hull. Torque an position sensors are place at the output shaft of the strain wave gearing. The position sensor has /unit resolution (16 bit per rotation). The velocity feeback is acquire fro the position feeback via nuerical ifferentiation. The otor control is ipleente on the Motorola s MC56F8323 series hybri 16-bit icrocontroller (MCU). The external interface to the joint organize through 125 Kbit CAN interface Torque sensor The torque sensor is a flange with three raial beas connecting the inner an outer rings as shown in the fig. 1(b). Microisplaceents in the aterial of the beas cause by the axial torque are easure with three pairs of stress gauges foring a half-brige. The strain gauges are place in such a way to iniize the influence of non-

3 1234 Victor Titov et al. / Proceia Engineering 69 ( 2014 ) axial torques an forces that are not aligne with the central axis of the sensor. The noinal torque of the both sensors (axiu esign torque of the sensor) is 75 N. (a) (b) Fig. 1. (a) two egree of freeo robot anipulator with torque sensors in the joints; (b) uni-axial torque sensor: 1-3 strain gauge pairs foring half-briges, 4 outer ring, 5 inner ring. The sae MCU as for the otor control with 12 bit ADC is use to easure three signals fro operational aplifiers an output the to the otors icrocontroller via I2C interface with 3kHz frequency (after preliinary filtration). Being integrate within the joint an having no hull of its own the torque sensor is vulnerable to istortions cause by ifferent parts of the joint echanics interacting with the strain waver gearing output shaft where the torque sensor is place. Due to these istortions the reaing of the unloae sensor fluctuates (zero reaing fluctuation) as angular position of the joint changes. The zero reaing fluctuation is shown in the fig. 2(a) against the angle of rotation. Fig. 2(b) shows the scale region of the curve pointe in the fig. 2(a). It is clear fro these two graphics that there is at least two types of istortions (apart fro usual fixe bias) an presuably two ajor source of the. (a) (b) Fig. 2. (a) fluctuation of the unloae torque sensor reaings (slow coponent); (b) scale region of the Fluctuation of the unloae torque sensor reaings (fast coponent is shown in bol). The first (slow) coponent (which is shown in the fig. 2(a) as an average fitting curve) changes slowly with the joint angular position an has the for close to sinusoial. Apparently the source of this istortion coponent situates soewhere on the output shaft. The sensory ata fro three half-briges show that the agnitue of this istortion in each signal is approxiately the sae but has phase shift for about 60 between any pair of signal out

4 Victor Titov et al. / Proceia Engineering 69 ( 2014 ) of three. The ost probable explanation for this is the output shaft curvature that akes the beas to ben along the rotation axes when all the strain gauges are subjecte to approxiately the sae eforation. Although the true source can harly be nae since there is no eans to isasseble an easure the eforation uring the shaft otion. The secon (fast) coponent (shown in the fig. 2(b)) has any perios within one joint revolution. For the joint with 100 reuction ratio of the strain wave gearing the perio of this curve is approxiately 3.6 of the output shaft. As the analysis of sensory ata fro the three half-briges show, this coponent of istortion anifests itself in all the three briges having ifferent sign, approxiately the sae agnitue but unstable phase shift between the three reaings. One can assue that the source of this istortion coponent lies soewhere in the echanical chain before the strain wave gearing or in the strain wave gearing itself. Thus exactly eterining the source of this istortion coponent sees even less possible than that of the slow coponent. Though the sources of the istortions are of great interest ore iportant is a practical way to copensate the. In the next section several ways to correct the zero reaing fluctuation are presente. 3. Torque Sensor Callibration An Zero Reaing Fluctuation Copensation Fro the escription of the torque sensor given in the previous section two tasks arise. The first is the correction of the sensor zero fluctuation. Being esigne for the noinal torque of 75 N the sensor has the agnitue of the zero fluctuation for about 2.5 N (that is 3.3% of noinal range). This accuracy gives only 30 iscreet steps of torque reaing in one irection. Such a situation is not goo enough for control purposes as well as for external torque registration. The other task is to fin the sensitivity of the sensor that converts easureent units into N (in the figures above this conversion has alreay been one for convenience of representation), i.e. calibration proceure Zero reaing fluctuation copensation Out of all possible ways to copensate the zero reaing fluctuation the ost reliable is the one using only the three signals fro the half-briges without aing any other feeback or assuptions about the istortions source oels. Another requireent one ay ipose on this etho is the copensation function to be a linear cobination of the three signals fro the half-briges. It is just logical since the true relationship between the source zero reaing fluctuation an its contribution to the three signal fro the half-briges stays unknown. In this situation the authors suggest to use the following as the output reaing of the sensor (1) u = k 0 + k 1 u 1 + k 2 u 2 + k 3 u 3 (1) where u 1, u 2, u 3 signals fro the three half-briges; k 1, k 2, k 3 scalar coefficients; k 0 fixe agnitue offset. Taking into account the properties of the istortions one can eterine the optial values for k 1, k 2, k 3 to be equal 1. That akes the correction into the siple average of the three signals. No nuerical optiization of k 0, k 1, k 2, k 3 gives any significant iproveent for the syste stuie. Unfortunately, this approach provies no ore than 1.9 ties reuction of the slow coponent an 1.2 of the fast coponent, in agnitue but as haronics to the curve ue to suation of the three. This happens ue to presence of non-sinusoial coponents in the istortion. Further reuction of the zero reaing fluctuations can be one by looking for the nonlinear correction function of three variables or by approxiating the curve with any etho available an subtracting it fro the output signal. The authors prefer the later as it is ore transparent an easily tune. Three approxiation techniques are consiere to be applie: polynoial, piecewise polynoial, piecewise linear. To choose aong this it is iportant to note that the function to be approxiate epens on the angular position of the joint output shaft. Also the torque reaing itself is require. Thus the only place where this coputation can be one is the joints MCU where the otor control is perfore an both values are available. As

5 1236 Victor Titov et al. / Proceia Engineering 69 ( 2014 ) this controller has excessive coputational resources to spent on control purposes the optial choice is piecewise linear approxiation. Points for piecewise linear approxiation are chosen at the local inia an axia of the fast coponent as shown in the fig. 3(a). There are totally 540 pair of points (positions, torque reaing) for the joint with 160 reuction ratio. The pairs are arrange in two arrays of 2 byte values for torque an position. Array inexation is one via siple hash function that eterines getting of the current shaft position into i-th interval in the position array. If current position is not close enough to one of the interval bounaries than the value of torque correction is copute accoring to (2) T(x) = T i + [T i+1 T i ] [x i+1 x i ]/[ x x i ] (2) where x current position; T(x) the value of correction; x i, x i+1 the beginning an the en of i-th interval; T i, T i+1 the correction value at the beginning an the en of i-th interval. This correction incorporates both the slow an the fast coponents. After the correction is applie the unloae torque sensor reaing fluctuation oes not excee 0.35 N (that is about 0.5% of the noinal torque). Fig. 3(b) eonstrates the unloae torque sensor reaing after correction against joint angular position. (a) (b) Fig. 3. (a) scale region of the zero reaing fluctuation: points of approxiation are arke as + ; (b) unloae torque sensor reaing fluctuation after correction Torque sensor calibration The calibration proceure is perfore by consequent loaing of the torque sensor with increasing/ecreasing payloa. There have totally been perfore ten series of increasing an ecreasing loaing cycles. First in one irection increasing series of loas was applie an the ecreasing series was applie straight afterwars. Such cycles was repeate five ties for each irection without alternating the irection for each series. The graphical representation of the results is show in the fig. 4. As one can see the sensor has goo linear characteristic. The conversion coefficient use in all the figures above was calculate to be 145 unit/n. Soe paraeters of the torque sensor suggeste in [5] a given in the Table 1.

6 Victor Titov et al. / Proceia Engineering 69 ( 2014 ) Fig. 4. Calibration graphic. Table 1. Torque sensor paraeters. Paraeters Value Sensitivity, units/n Repeatability, units 119 Resiual value at zero torque, units 18 Maxial eviation of inication fro the fitting curve, units Moel of the joint with torque sensor In this section a siplifie atheatical oel of the joint with torque sensor necessary is given for control schees explanation purpose. Although a torque rive is a synchronous 3-phase achine it can be approxiate with the oel of a stanar DC otor (3). ( t) C i ( t); e( t) C e ; (3) u( t) e( t) R i ( t) ( i ( t) / t) L; J ( t) ext ( t) fric(, ext, t); where otor torque; C,C e electrical an torque constants of the otor; e EMF; R,L resistance an inuction of the rotor; J rotor inertia; ext external torque;, secon an first erivatives of the rotor angular position, ( fric, ext, t) friction, u supply voltage; i otor current. The friction force has two coponents: static an ynaic. The first represent the friction behavior before otion starte. In general this can be expresse as (4) (see [6]) fric S ext F sign( F(, t), if, if, ext ext F ), otherwise S (4) where sall value representing inial velocity still eee as zero; F s the value of static friction; F(, t) ynaic friction oel (in this work the LuGre oel i use). For siplicity the strain wave gearing is assue to be infinitely stiff. The only copliant eleent in the syste is the torque sensor. It is oele as follows

7 1238 Victor Titov et al. / Proceia Engineering 69 ( 2014 ) C ( / r q); J loa q D C 1 ext (5) where С the torque sensor stiffness ; J loa payloa inertia; D viscous friction coefficient of the sensor aterial; bening torque of the sensor; q the angular position of the sensors output shaft; ext external torque applie to the sensor; r reuction ratio. Using (5) ext in (3) is eterines as (6) ext D C 1 (6) The graphical representation of the oel is shown in the fig Approach to control Fig. 5. Moel of the joint with torque sensor (s = /t). Force control is alreay a ajor fiel in robotics. The outline of the control strategies an their applications can be foun in [7]. The control probles arising that can be et in literature ainly concern the elasticity of the torque sensor an its influence on the control ynaics. In a particular lots of authors point out two tie scale ynaics of the flexible joint robot (FJR). The first oel of elastic joint robot was propose by Spong [8]. Since then nuerous controllers was propose soe of which are outline in [9]. In this work one of the classical robot control architecture incluing two (lower an upper) levels of control was aopte. The upper level of control generate require values of torque which are coane to the lower level an processe by each joint inepenently. Such control architecture loses to the one with centralize coputation in quality but wins significantly in siplicity while aking oule principle possible Joint level torque control For the purposes of controlling the robot two types of torque controllers are use at the joint level. The torque control loop functioning at 1 khz frequency while feeback is saple an preprocesse at 3 khz. The first one is base on the research publishe in [10] an ipleents a passive aaptive torque controller. Assuing that the control of otor current is at least 10 ties faster than the torque control loop (that is quite true) an one can coan the require current irectly neglecting the current transient, the torque controller can be expresse as (7)

8 Victor Titov et al. / Proceia Engineering 69 ( 2014 ) i K K K ( ) K K ˆ (7) i i p i where i esire current value for the current control loop; K i conversion coefficient fro current to otor torque; K p proportional gain; K aping; current value of the torque sensor easureents; the esire torque prouce by the upper level; ˆ an estiation of the torque first erivative obtaine using secon orer torque observer (8). ˆ k ˆ k T ˆ 1 k l1 1 ˆ k 0 0 ( ˆ k ) l 2 (8) where l 1,l 2 scalar coefficients ensuring require filtering level; T 1 sapling perio. This controller has several qualities that ake it convenient in application. First it is relatively siple an can be tune intuitively by iteratively searching for its coefficients. It also has steay state (static) errorthat is both avantage an isavantage of this controller. Although having static error akes this controller less preferable when accurate torque control is neee this error can be very useful when ealing with uncertainty of that frequently leas to the anipulator instability. An exaple of such instability is an attept to copensate for gravity torque having uncertain ass paraeters. Trying to fee the copute gravity torque to the torque controller in this case causes the anipulator to enlessly waner in search of the equilibriu point (where ). Thus the stability can t be ensure on the whole range of the joint positions. Having static error solves this proble at the cost of accuracy an syste sensitivity. The other controller uses inner velocity loop. It is fairly easy to see fro the joint oel in the fig. 5 that in the static case (when the output shaft of the sensor is blocke) controlling the torque reuces to controlling the position of the strain wave gearing output shaft. In general it is also true as the torque at the sensor can be expresse as the ifference between the strain wave gearing output shaft position an the torque sensor output shaft position. Thus controlling the otor velocity is equal to controlling sensor torque erivative in the static case. In the control schee propose in this paper there is four control loops in linear hierarchy (the ost inner loop is the first; see fig. 6): current loop; velocity loop that uses PI regulator to coan the current loop; torque loop that uses P regulator to coan the velocity loop; non linear aping loop that also coans the velocity loop. Without aitional aping the syste gets the property of echanical energy accuulator. Such syste woul hol its velocity until external torque is applie. To avoi this while saving goo transient behavior the non-linear aping of the for (9) is applie. ep K D (,, ) (9) k 1 ec where K D the axial value of the aping coefficient; k ec coefficient eterining how fast the aping is ecreasing as the torque error is increasing. Such a aping offers goo stability at the τ point while saving the sensitivity. This controller has no static error an approxiately the sae stability as the first one. Such properties are the result of correction introuce by the inner loops (current, velocity). In the case of uncertain τ this controller is harly applicable to gravity copensation since it woul try to track τ no atter how far the true equilibriu is. When the fast an accurate torque control is neee this controller gives goo results an is relatively easy to tune. In the fig. 6 the esire velocity for the velocity control loop; T1 feeback sapling rate; T2 velocity an torque control signal generation rate.

9 1240 Victor Titov et al. / Proceia Engineering 69 ( 2014 ) Upper level control Fig. 6. Torque controller with inner velocity loop. For this control level two types of control strategies are teste. The first control strategy is the force/torque control with gravity copensation with aitional aping. The esire torque vector (2 coponents) is fore as (10) τ = G(q) K ep q (10) where q the vector of the sensors output shaft angular positions; q the vector of its first erivatives; K ep aping factor; G gravity torques coputation function. For this control strategy the passive aaptive torque controller is use ue to the reasons iscusse in the previous subsection. Main application of such a control strategy is to anually for a trajectory for the anipulator. The low accuracy of the joint level torque controller in this case poses certain ifficulty for using the control strategy to coan otion of exact force task (though if accuracy is not as iportant as safety this strategy can be use this way). The other control strategy ipleente on this level of control is partial ipeance control. As known for exaple fro [7] to fully ipleent ipeance control one nee to provie esire position along with its first an secon erivatives as well as the sae set of values in feeback. Acceleration easureent for the syste has prove to be very ifficult to obtain accurately. For this reason just liite version of ipeance control is ipleente (11). τ = G(q) + J(q) [S (q q) + D ( q )] (11) q where J(q) inertia atrix of anipulator (provies partial ecoupling); S proportional gain (or stiffness coefficient); D aping factor; q the vector of esire positions; q the vector of its erivatives. For this control strategy at the joint control level the controller of the secon type (with inner velocity loop) is use. This strategy gives goo positional accuracy (the better the bigger proportional gain S) an can provie significant copliance (without loss of accuracy if gravity copensation is copute). In ynaics (when q 0 ), proviing control syste with q significantly increases the accuracy of trajectory tracking at the cost of increasing coplexity of the upper level. This control strategy is ainly use for safe anipulation tasks that requires consiering the presence of unknown obstacles in the operational space. In [11] another approach to the force-position control of the 8 DoF robotic ar is presente. In contrast with the syste in the present paper only one 6 DoF force/torque sensor is place at the wrist of the ar. The authors ipleente a classical force control schee with internal position-close loop. Though goo position an force tracking accuracy is grante the significant rawback of this approach is poor ynaic characteristics for force tracking (the approxiate tie constant is about 0.2 sec. while the tie constant for our robot is less than 0.08 sec.). Poor ynaic characteristics in [11] are the result of closing the force loop on the upper control level which is uch slower that use for position control. In our case the reverse schee (with force/torque control at the lower level) proves to be ore efficient.

10 Victor Titov et al. / Proceia Engineering 69 ( 2014 ) Conclusion an iscussions In this paper, a coplex of the probles concerning force/torque control was solve for a 2DoF robot anipulator use as exaple. Two ajor coponents of force/torque control for the robot was stuie: torque ata acquisition an control law forulation. In the torque ata acquisition a solution for the proble of zero reaing fluctuation of a ebee toque sensor was presente. The propose correction shows significant iproveent of the sensors accuracy (the fluctuation agnitue ecrease ore than 7 ties in coparison with the raw signal). For the torque sensor after zero reaing correction the results of calibration proceure was presente. Two joint level torque controllers were presente an iscusse with their relation to the upper level control strategies. It was shown that static torque error introuces by a passive aaptive torque controller at the joint level ensures goo stability properties when use with force/torque with gravity copensation control strategy at the upper level control. A torque controller with velocity inner loop shows no static error an better ynaic characteristics an proves to be useful in ipeance control strategy. Although the evelope controllers fro the basis for force/torque control they still lack certain properties that woul give the wier application fiel. One of the serious probles in controlling anipulator with any egrees of freeo is significant epenence of the inertia paraeters of the latter on the links positions. For the joint torque control syste this leas to the changes in payloa inertias with joints positions an as a result to the shift of the controllers optial paraeters. To hanle this proble an aaptive echanis shoul be applie in each joint to ajust the paraeters. Aaptive structure of the joint torque controller can also enforce the oule principle an ake each joint interchangeable. Developing the aaptive controllers is one of the irections for the future work. The correction of the torque easureent for the ebee sensor propose in the papers generally iproves the quality of the torque control but cannot be eee as the final option since there is no guaranties that the for of copensation signal oes not change with tie. Ieally the eliination of the istortions sources woul be the optial solution. To achieve it the sensor construction shoul be reconsiere. Also, though in the present paper the zero reaings fluctuation correction prove to be unreovable with just raw signals processing it oesn t ean that this rather attractive way cannot be use. Correct placeent of the strain gauges (or/an probably aing several new strain gauges pairs) along with ore coplex signal processing ay lea to uch better results even without changing the sensor construction. The research of such possibilities is still to be one. The evelopent of the robot ar an the control syste was carrie out with the financial support of the Ministry of Eucation an Science of the Russian Feeration. References [1] es%3d1976_2014_p_publication_year%26rowsperpage%3d100%26querytext%3dforce+control+robotics&pagenuber=82 [2] [3] A. Albu-Schäffer, S. Haain, Ch. Ott, A. Steer, T. Wiböck, G. Hirzinger, "The DLR lightweight robot: esign an control concepts for robots in huan environents", Inustrial Robot: An International Journal, Vol. 34 Iss: 5, 2007, pp [4] [5] EURAMET/cg-14/v.01: Guielines on the Calibration of Static Torque Measuring Devices, rev.00, July, 2007 [6] Olsson H., Åströ K.J., Canuas e Wit C., Gäfvert M., Lischinsky P., «Friction Moels an Friction Copensation,» Eur. J. Control, т. Vol. 4, 3, pp , [7] Siciliano, B., Sciavicco, L., Villani, L., Oriolo, G. Robotics. Moelling, Planning an Control, 2n Printing., 2009, Springer-Verlag, XXIV, 632 p. 298 illus., ISBN [8] Spong, M.W., Moeling an Control of Elastic Joint Robots, J. Dyn. Syst., Meas., Contr.(1987). [9] Ozgoli S., Taghira H. D., A survey on the control of flexible joint robots, Asian Journal of Control, Vol. 8, No. 4, pp. 1-15, Deceber [10] Albu-Schaffer A., Ott C., Hirzinger G., «A passivity base Cartesian ipeance controller for flexible joint robots - part II: full state feeback, ipeance esign an experients,» [11] Giovanni Geraro Muscolo, Kenji Hashioto, Atsuo Takanishi, an Paolo Dario, A Coparison between Two Force-Position Controllers with Gravity Copensation Siulate on a Huanoi Ar, Journal of Robotics, vol. 2013, Article ID , 14 pages, oi: /2013/