Control of Generalized Contact Motion and Force in Physical Human-Robot Interaction

Transcription

1 15 IEEE International Conference on Robotics an Automation ICRA Washington State Convention Center Seattle, Washington, May -3, 15 Control of Generalize Contact Motion an Force in Physical Human-Robot Interaction Emanuele Magrini Fabrizio Flacco Alessanro De Luca Abstract During human-robot interaction tasks, a human may physically touch a robot an engage in a collaboration phase with exchange of contact forces an/or requiring coorinate motion of a common contact point. Uner the premise of keeping the interaction safe, the robot controller shoul impose a esire motion/force behavior at the contact or explicitly regulate the contact forces. Since intentional contacts may occur anywhere along the robot structure, the ability of controlling generalize contact motion an force becomes an essential robot feature. In our recent work, we have shown how to estimate contact forces without an explicit force sensing evice, relying on resiual signals to etect contact an on the use of an external epth sensor to localize the contact point. Base on this result, we introuce two control schemes that generalize the impeance an irect force control paraigms to a generic contact location on the robot, making use of the estimate contact forces. The issue of human-robot task compatibility is pointe out in case of control of generalize contact forces. Experimental results are presente for a KUKA LWR robot using a Kinect sensor. I. INTRODUCTION In the robotics community at large, there is great excitement about the recent possibility of realizing safe physical collaboration between human users an a new inustrial generation of lightweight, compliant, an frienly robots [1], []. This technical achievement is the outcome of avances in mechanics, actuation, sensing, an control that have emerge in the last few years, from statements of basic requirements see, e.g., [3] [] to novel research results see, e.g., [7], [] for the original collision etection algorithm implemente in the KUKA LWR an iiwa robots. Inee, more of such scientific evelopments an technological transfers are neee in orer to improve further the autonomy, safety, an ease of use of robotic coworkers in inustrial settings an of personal assistants in service applications. Along this path, we have propose a control architecture for safer physical human-robot collaboration, base on a hierarchy of three consistent robot behaviors [9]. In this framework, safety is the innermost layer with the highest priority of execution: it implies the ability of etecting an fast reacting to acciental collisions [1] an istinguishing between these an intentional contacts [11], [1]; coexistence is the robot capability of sharing workspaces, without interfering with humans: it calls for collision avoiance features [13], [1], an robot operative flexibility for The authors are with the Dipartimento i Ingegneria Informatica, Automatica e Gestionale, Sapienza Università i Roma, Via Ariosto 5, 15 Roma, Italy {magrini,fflacco,eluca}@iag.uniroma1.it. This work is supporte by the European Commission, within the FP7 ICT-7513 SAPHARI project moifying on line, abanoning, an resuming the originally planne tasks; finally, collaboration requires the robot to perform complex tasks involving irect physical interaction an coorination with humans. One can consier ifferent possible collaborative tasks where physical human-robot interaction occurs: carrying a heavy payloa, haning over objects, manipulating limp materials, holing firmly a part while the partner is operating on it, an so on. In most cases, regulation of the forces exchange at the contact is neee an/or accurate control of relative motion while keeping in place the original contact. As aitional convenient features, whole-boy manipulation shoul be possible, with single or multiple contacts occurring anywhere along the robot structure, an a minimum amount of extra sensing shoul be requeste, in particular without the nee of a F/T sensor at the wrist or of istribute tactile sensing for the measurement of contact/interaction forces. In [15], a metho has been evelope for estimating the interaction forces in irection an intensity uring ynamic contacts between a robot an a human, with no explicit force/torque sensing. The metho is base on the integrate use of moel-base resiual signals that etect the occurrence of collisions [] an of one or more external RGB-D sensors e.g., Kinects to approximately localize the contact point on the surface of the robot links. This virtual force sensor was shown to perform with reasonably goo estimation accuracy. Its output has been use alreay in a series of humanrobot interaction experiments base on an amittance control scheme efine at the contact point. In this paper, we illustrate further the use of the estimate contact forces for the esign of two human-robot interaction controllers that exten the impeance control metho [1] an the irect force control metho [17], respectively to the case of generic contact locations on the robot. For this reason, we collectively enote this approach as generalize contact motion an force control. While irect force control nees always a measure or an estimate of the contact force, stanar joint or Cartesian impeance control laws require a force measure only if the natural robot inertia at the proper level has to be change to a esire one. When the robot inertia is left unchange, force sensing is no longer require the term compliance control shoul be use then. The same situation hols true also for our generalize contact impeance control laws, simply replacing actual measurements with the use of force estimates see also Fig. 1. When realizing a force control law at the contact level, task compatibility issues may arise, mainly ue to the /15/$ IEEE 9

2 k F Fc k " k F m F c k " "#$%&"#$%&'$ '$$%*+,'--,./$*$'*,.* F c F ˆ c '"$%%&#,'-"#$%&'$ 1-,-3,.$-,./$*$'*'5 1-$*7"&7,',3-$,'-&-3,.$ '*%+,#$&"#$%&'$ '$$%*91.*-*$'*,. " k Fig. 1. A schematic comparison of impeance control schemes for a fully rigi robot arm, when a esire mass-spring-amper behavior is impose at the joint-level, at the Cartesian-level, or at the propose contact-level, in response to a contact force F c. The estimate contact force F b c can be obtaine with the metho in [15]. generality of the possible locations of the contact point. A first reason follows from the arguments alreay presente in [15]. When contacts occur on a link close to the robot base, the estimation metho may have too little information to recover a complete estimate of the applie contact force in particular, the contact Jacobian may not be full rank. The secon reason is even more funamental, an refers to the type of engage human-robot contact an its compatibility with the specification of a esire contact force. A complete specification of three inepenent scalar references for the contact force may be incompatible with the way the human is pushing on the robot. The situation is similar to efining a correct task frame in hybri force/motion control [1], [19, Chap. 9. 7]: the robot cannot control forces along contact irections where the human is not proviing a reaction. While the contact amittance control scheme in [15] specifies joint velocity references in response to estimate contact forces, an relies upon low-level servo loops for their execution, the two control esigns presente in this paper generate torque commans, an assume thus a torquecontrolle robot viz., motor currents can be impose. In aition, an accurate robot ynamic moel will be neee for control implementation. All evelopments in the paper are presente for rigi robot manipulators. Accoringly, no joint torque sensors are use nor neee an the virtual force sensor concept an the associate contact force/impeance controllers can be implemente using only the joint encoers as proprioceptive sensing. On the other han, the presente control experiments have been performe on a KUKA LWR where the use of harmonic rive introuces joint elasticity []. In practice, however, the control implementation for this robot is fully transparent with respect to the presence of compliant joints. The user efine torque-controlle moality of the FastResearchInterface FRI [1] implements the torque controller originally propose in [], an allows to use the available joint torque sensors both for resiual computation an for control. Moreover, for all moel-base computations we have use our own ientifie ynamic moel of the LWR link ynamics [3]. The paper is organize as follows. Section II sets the notation an inclues a short summary on the contact force estimation metho [15] use in the remainer of the paper. Section III recaps in a compact way the stanar impeance an irect force control laws for a single mass subject to an external contact force. The generalization of these control schemes to hanle contact situations occurring at a generic point of a multi-of robot manipulator is etaile in Sec. IV. Section V reports on several experimental results obtaine with the propose control methos uring physical humanrobot interaction with a KUKA LWR robot an a Kinect sensor. II. PRELIMINARIES For a robot manipulator having n serial joints, with associate generalize coorinates q R n, assume that a motion/force interaction task is efine for a contact point x c R 3 whose irect kinematics map is given by x c = fq. Differentiating this twice w.r.t. time yiels ẍ c = J c q q + J c q q, 1 where J c = fq/ q is the 3 n contact Jacobian matrix. Note that if the contact point is locate on link k k = 1,..., n, the last n k columns of J c will be ientically zero. In most cases, the robot is reunant respect to the given interaction task, being k > 3. At a given robot state q, q, all joint accelerations associate to a esire acceleration ẍ c of the contact point can be written as q = J # c ẍ c J c q + P c q, where J # c is a n 3 generalize inverse of the contact Jacobian, q R n is an arbitrary joint acceleration, an P c = I J # c J c is a projector in the null space of J c. The ynamic moel of a rigi manipulator interacting with the human environment at a robot point x c is given by Mq q + Cq, q q + gq = τ + J T c qf c, 3 with positive efinite inertia matrix M, Coriolis an centrifugal velocity terms C q factorize by the Christtoffel symbols, gravitational terms g, control torque τ R n, an joint torque τ c = J T c qf c resulting from the contact interaction force F c R 3. We will use also the compact notation nq. q = Cq, q q + gq. In the framework of operational space control [1], it has been shown that using the inertia-weighte pseuoinverse as the generalize inverse in guarantees consistency of 99

3 the transformation of task forces in the robot ynamics. The inertia-weighte pseuoinverse of contact Jacobian is J # c,m = M 1 J T c J c M 1 J T c 1. In the following, to simplify notation, each pseuoinverse J # c is to be intene as the inertia-weighte one given by. A. Contact force estimation The resiual vector r R n for a robot with ynamics 3 is efine as [7] t rt = K I p τ + C T q, q q gq + r s, 5 where p = Mq q is the generalize momentum of the robot an K I > is a iagonal gain matrix. The ynamic evolution of r has the stable, first-orer filter structure ṙ = K I τ c r. Thus, for sufficiently large gains, we can assume that r τ c = J T c qf c. Equation forms the basis for the estimations of the unknown contact force F c R 3. Using external sensing, the location of the contact point x c can be etermine, an thus the associate contact Jacobian J c can be compute. Depening on which link in the kinematic chain is involve in the contact, may consist of a square, uner-, or overetermine linear system. In any case, the contact force is estimate by pseuoinversion as F c = J T c q #r. 7 Inee, the estimate F c will be limite only to those components of F c that can be etecte by the resiual r, namely those contact forces that o not belong to the null space N J T c q. For further etails an for the analysis of cases when the contact Jacobian is not full rank, see [15]. III. IMPEDANCE AND FORCE CONTROL FOR A SINGLE MASS As an introuction to the control esign for the general multi-of robotic case, consier first a very simple 1-of example. As shown in Fig. 3, a single mass m moves on a frictionless horizontal plane uner the action of a control force f an of a contact force f c. The ynamic equation is mẍ = f + f c. Fig. 3. A mass m subject to a control force f an a contact force f c. A. Impeance control The inverse ynamics control law f = ma f c, 9 transforms system into the ouble integrator ẍ = a. 1 The auxiliary input a has to be esigne so that the controlle mass m, uner the action of the contact force f c, matches the behavior of an impeance moel characterize by a esire apparent mass m >, esire amping k >, an esire stiffness k p >, all with respect to a smooth motion reference x t, or m ẍ ẍ + k ẋ ẋ + k p x x = f c. 11 This is obtaine by using the control force f = m m ẍ + k ẋ ẋ + k p x x+ 1 f c. m m 1 For k < k pm, the secon-orer linear system 11 is characterize by a pair of asymptotically stable complex poles with natural frequency an amping ratio given by Fig.. A view of the result of the on-line estimation of the contact force ω n = kp k, ζ = m. 13 k p m Reucing the esire mass m, for given values of stiffness an amping, will increase both the angular frequency an the amping ratio, an thus improve transients. On the other han, for a given mass, an increase of the stiffness k p shoul be accompanie by an increase of the amping k in orer to prevent more oscillatory transients. If the esire mass equals the natural original mass, i.e., m = m, a measure of the contact force f c is no longer neee in the impeance controller 1 which is then also calle a compliance control law, since the main esign parameter left is the esire stiffness k p. In particular, for 3

4 regulation tasks with x t = x = constant the control law collapses just to a PD action on the position error e = x x, f = k p x x k ẋ. 1 The system will converge to x = x if an only if there is no contact force. With f c but constant, there will be convergence to the close-loop equilibrium x e satisfying k p x x e + f c = x e = x + f c k p. 15 B. Force control If we esire to control irectly the contact force to a esire possibly, constant value f, it is necessary to buil a force error e f = f f c into the control law. After using eq. 9, efine the auxiliary input a as a = 1 m k f f f c k ẋ 1 with force error gain k f > an velocity amping k >. The associate control force is then f = m m k f f f c k ẋ f c. 17 A contact force measure is always neee in this case, even if we choose m = m. The close-loop system becomes m ẍ + k ẋ = k f f f c, 1 which shows that the force error e f goes to zero if a constant contact force is applie. However, the actual position x = x e reache at the equilibrium is not known a priori, an will epen on the actual history of the external contact force. IV. GENERALIZED CONTACT MOTION AND FORCE CONTROL FOR ROBOTS We exten here the control esign results of Sec. III to a generic robot contact point x c of a robot manipulator, an consier also the use of the contact force estimation F c, as provie by 7, in place of the real measurement, each time this will be neee. A. Impeance control Starting from robot moel 3, an ropping from now on epenencies for the sake of compactness, consier the inverse ynamics control law τ = Ma + n J T c F c, 19 where F c is the estimate contact force. In ieal esign conitions, the above control law realizes a feeback linearization, leaing to a system of ouble integrators q = a. The auxiliary control input a is chosen so as to impose a mechanical impeance moel between the estimate contact forces F c an the motion of the contact point x c, or M ẍ c ẍ + K ẋ c ẋ + K p x c x = F c, being M > the esire inertia matrix, K > the esire amping matrix, K p > the esire stiffness matrix very often, these matrices are taken as iagonal, an x t the smooth esire trajectory of the contact point. Solving for ẍ c from an using, the control input a is obtaine as a=j # c M 1 M ẍ +K ė+k p e M J c q+ F c +P q, 1 with contact position error e = x x c. Thus, the resulting torque control input is τ = MJ # c M 1 M ẍ + K ė + K p e M J c q + F c + MP q + n J T F c c. In, observe that the contribution of F c is given by τ =... + MJ # c M 1 J T c F c. 3 As expecte, when choosing the esire inertia matrix M equal to the natural Cartesian inertia of the robot at the contact point, also the estimation of the contact forces F c will no longer be neee. At a given configuration q, the natural inertia of the robot at a generic contact point is 1 M = J c M 1 J T c. By using, it is easy to see that MJ # c M 1 J T c =. Whenever we esire to impose a ifferent inertial behavior at the contact, e.g., so as to achieve ifferent behaviors in ifferent irections of the operative space, we shall make use of the contact force estimate F c. B. Force control The impeance metho realizes only an inirect control of the forces exchange uring the interaction with the human, ynamic balancing with the esire position x c of the contact point. The evelopment of a irect controller for the contact force is crucial for collaborative tasks that nees accurate execution in uncertain conitions. With the reference to 19, choose in place of the auxiliary comman 1, the following acceleration a = J # c M 1 K f F F c K ẋ c M J c q +P q, 5 where F is the esire force at the contact point, the contact force error is e f = F F c, an K f > is the force error gain matrix. Replacing 5 in 19, the final torque control input is τ = MJ # c M 1 + MP q + n J T c F c. K f e f K ẋ c M J c q Similarly to 1, the close-loop system is escribe by M ẍ c + K ẋ c = K f F F c, 7 which shows again that the force error shoul go to zero whenever a constant contact force is applie. Nonetheless, the issue of task compatibility remains open. In the above expression of the control law for the human-robot contact forces, the specification of the esire force F is apparently an unconstraine one. We shall see in the experiments that 31

5 a careful choice of F shoul be mae so as to avoi inconsistent an rifting behavior of the robot, with serious consequences for safety. " V. E XPERIMENTAL RESULTS $" Fig.. The set-up an the Cartesian reference frame for the contact impeance control experiments. The color of the X, Y, an Z axes are the same use for the associate components in the following plots. 15 Resiual [Nm] 1 Similarly for the force control law it is 1 τ = MJ# K f ef K x c M J c q c M b c. M P K N q + C q J Tc F 5 r1 15 r r3 r r5 r r Fbc,x b c. M P K N q + C q J Tc F 5 1 Fbc,y Fbc,z.. 9. Error [m] c #" Dynamic human-robot interaction experiments using the propose controllers have been performe on a KUKA LWR. The workspace is monitore by a Microsoft Kinect epth sensor, positione at a istance of 1.7 m behin the robot an at a height of 1.1 m w.r.t. the robot base frame. The Kinect provies epth images at 3 Hz rate. All algorithms are execute on a qua-core CPU. The complete process of contact force estimation an motion an/or force control run on the robot at 5 ms cycle time. With reference to the impeance control law, efine x = xc tc R3 as the initial an constant position of the contact point when the interaction with the human begins at t = tc. The esire velocity an acceleration are =. Due to the reunancy of this set then to zero, x = x robot with respect to many tasks, a null-space acceleration = K N q, with K N >, in vector has been chosen as q orer to boun/amp out self-motion movement of the arm. Finally, recall that the KUKA LWR has a built-in gravity compensation. Thus, the actual impeance control law use to comman the robot was bc τ = M J # M 1 K p e K x c M J c q + F All experiments presente in this paper are recore in the accompanying vieo clip. The plots can be even better appreciate when looking in parallel at the vieo.. ex ey ez A. Impeance control with natural contact inertia In the first experiment, the human pushes the robot at ifferent contact points an on ifferent links, as shown in the snapshot of Fig.. The control law is given by, with the esire inertia matrix at the contact chosen equal to. The other impeance parameters were set to K = I 3, K p = 5 I 3, an K N = I 7, where I k enotes the k k ientity matrix. Figure 5 shows the behavior of the resiual vector, of the contact force estimate, an of the Cartesian position error of the contact point with respect to its initial position x = xc tc. B. Impeance control with moifie contact inertia In this experiment, the impeance scheme was use again uring the human-robot interaction. However, the esire inertia matrix at the contact point was set to M = 3, 1 Fig. 5. Contact impeance control with esire inertia matrix at the contact equal to the natural one. Resiual vector components [top]. Estimate contact force components [center]. Contact position error components [bottom]. i.e., ifferent from the natural one which was also couple. Non-uniform values were chosen on the iagonal, so as to obtain ifferent behaviors along the three Cartesian axes see also Fig.. To enhance this effect, the human pushes the robot always on link, although in ifferent irections. The other impeance parameters use were the same as in Sec. Vb c are neee A. In this case, the estimate contact forces F by the control law in orer to obtain the esire mass-springamper system. Figure shows the same quantities of the previous impeance control experiment. When the contact is initially etecte, the robot will move the contact point with a ynamics that epens on the irection of the external force. When the han is remove, the robot brings back the contact point to the original initial position. As shown in Fig. thir 3

6 plot, the error returns closer to zero on the y axis, where M,y = 3. By increasing the esire inertia, the error natural frequency an amping ecrease, as inicate by 13, an transients will worsen see, e.g., the x axis at t = 15 s. " #" $" 3 Resiual [Nm] 1 1 r 1 r r 3 r r 5 r r Fig. 7. The set-up an the Cartesian reference frame for the contact force control experiments. On the left, the human is pushing along the Y irection where a non-zero esire force is specifie F y, = 15 N. On the right, a rift effect occurs ue the absence of a human reaction in the Y irection a force is applie approximately along the X irection only. Error [m] F c,x Fc,y Fc,z Fig.. Contact impeance control with moifie inertia matrix at the contact. Resiual vector components [top]. Estimate contact force components [center]. Contact position error components [bottom]. C. Contact force control with possible rift effects The purpose of this experiment was to show that it is highly not recommene to try to regulate human-robot contact forces at arbitrary values an in multiple fixe irections of the Cartesian space. When the human oes not push or resist along a irection where a non-zero force reference has been specifie, the robot typically rifts in space in the attempt to regulate the incompatible esire force. This coul be angerous because an unexpecte movement occur, through which the robot may collie with the human. With this in min, the parameters were set to K = 1.5 I 3, K f =.1 I 3, K N = 15 I 7, an the esire contact force was chosen as F = 15 T, i..e., only in the Y irection. Figure shows the behavior of the resiual vector r, of the contact force estimate F c, an of the Cartesian velocity ẋ c of the contact point. When the human pushes the robot on link along the Y axis, the robot reacts properly an regulate the force components to the esire level. However, when the human pushes the robot along the X irection, a rift occurs along the Y irection, as shown in Fig. e.g., at t = 1. s. D. Contact force control with task compatibility The contact force control scheme 9 was use in this interaction control experiment, where the human pushes the e x e y e z Resiual [Nm] Velocity [m/s] r 1 r r 3 r r 5 r r F c,x Fc,y Fc,z F,y ẋ c,x ẋ c,y ẋ c,z Fig.. Contact force control with rift motion ue to task incompatibility. Components of the resiual vector [top]. Moulus of the estimate contact force [center]. Components of the Cartesian contact velocity ẋ c [bottom]. When the human pushes along the Y irection, regulation occurs see the first 1 s. The human pushing along the X irection where F x, = will be accommoate by a robot retraction, whereas the absence of a human reaction in the Y irection where F y, = 15 N oes not allow force regulation an generates large velocity rifts in that same irection see the last s in the thir plot. robot successively on link 3, link 5, an then link see the associate behaviors of the resiuals in Fig. 9, [top]. To avoi incompatibility with the human, only the norm of the esire contact force F has been, here as a constant F = 15 N. However, F will change irection accoring to the human-robot contact type, an being always aligne with the estimate contact force vector which may now vary without any restriction. We will have thus, F,x = 15 F c,x F c, F,y = 15 F c,y F c, F,z = 15 F c,z F c. 33

7 The other force control parameters use were the same as in Sec. V-C. Figure 9 shows the same quantities of the previous force control experiment. Note that the controller starts operating after the first etection of a contact. When the human pushes the robot, it gets compliant in orer to regulate the contact force at the esire value. When the human tries to recee, the robot pushes against the human han so as to maintain the esire F c = F. The fact that the human may abanon the contact an then resume it in a ifferent point an along a ifferent irection is no longer a problem for this correctly efine contact force controller. On the other han, this force control law is able to regulate contact forces only in static conitions i.e., when ẋ c =. While the human is moving the robot uring a contact, some error will result as shown in Fig. 9. Resiual [Nm] Velocity [m/s] r 1 r r 3 r r 5 r r F c F ẋ c,x ẋ c,y ẋ c,z Fig. 9. Contact force control is here esigne for automatic task compatibility. Components of the resiual vector [top]. Moulus of the estimate contact force [center]. Components of the Cartesian contact velocity ẋ c [bottom]. VI. CONCLUSION We have expane the portfolio of controllers for physical human-robot interaction tasks, introucing the concept of motion an/or force control at any contact point on the robot. Generalizations of classical impeance an irect force control schemes have been introuce an implemente without the explicit nee of a force sensor, relying on a fast estimation of contact forces. Besie eveloping an refining further such basic robotic skills for safe collaboration, our next step will be their application to concrete an specific tasks e.g,, performing human-robot collaborative assembly within the inustrial use cases of the SAPHARI project. We also wish to exploit the robot reunancy for controlling motion in the plane perpenicular to the estimate contact force i.e., achieving hybri force-motion control. 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