Fuzzy Learning Variable Admittance Control for Human-Robot Cooperation

Transcription

1 Fuzzy Learning ariable Amittance Control for Human-Robot Cooperation Fotios Dimeas an Nikos Aspragathos Abstract This paper presents a metho for variable amittance control in human-robot cooperation tasks, that combines a human-like ecision making process an an aaptation algorithm. A Fuzzy Inference System is esigne that relies on the measure velocity an the force applie by the operator to moify on-line the amping of the robot amittance, base on expert knowlege for intuitive cooperation. A Fuzzy Moel Reference Learning Controller is use to aapt the Fuzzy Inference System accoring to the minimum jerk trajectory moel. To evaluate the performance of the propose controller a point-to-point cooperation task is conucte with multiple subjects using a KUKA LWR robot. I. INTRODUCTION Avances in robot control have enable the cooperation between robots an humans through active compliant motion control of manipulators. Assisting robots that interact physically with a human can enhance the physical capabilities of the latter an can facilitate everyay tasks e.g. manipulation of heavy or long bulky objects. Particularly in inustry, where assembly of heavy parts requires the high flexibility of the human, a cooperative manipulation woul facilitate the task since it will reuce the buren from the human. Impeance control [1] is wiely use in physical humanrobot interaction (phri), since it has the ability to establish a ynamic relationship between the robot an the environment. Instea of controlling the position or the force inepenently, the ynamic behaviour of the robot is regulate by moifying the parameters of virtual stiffness, amping an inertia. In human-robot collaboration, where the robot oes not usually interact with stiff environments, amittance control is incorporate, which creates a mapping from forces into motion enabling the robot to comply to any forces applie by the human at a preefine manner. Since it was shown that the most ominant parameter of amittance control in human-robot collaboration is the virtual amping [2], a lot of research has been conucte on tuning this factor for more intuitive interaction. A variable amittance control scheme was introuce in [3] to aapt the amping factor with respect to the spee of the cooperation. Duchaine et al. [4] ajuste the amping by estimating the human intentions from the ifferentiation of the force applie by the operator to the robot. A combination of the operator s velocity an acceleration was propose in [5], however numeric ifferentiations yiel noisy signals that require filtering an cause elays. Although the results with Authors are with the Robotics Group, Dept. of Mechanical Engineering & Aeronautics, University of Patras, 265 Patra, Greece. Fotios Dimeas is fune by IKY fellowships of excellence for postgrauate stuies in Greece - Siemens program. {imeasf,asprag}@mech.upatras.gr variable amittance on the mentione papers emonstrate superior performance compare with constant amittance parameters in terms of intuitiveness, precision an transparency of motion, the functions that tune the parameters are obtaine accoring to the researcher s intuition an in a heuristic manner. A more systematic approach for aapting the robot amittance was propose by Rahman et al. [6] who investigate the human arm characteristics. The authors ientifie the human arm impeance in a human-human cooperation task an erive a function to tune the robot amping accoringly for a similar human-robot task. A metho to on-line estimate the human arm stiffness an ajust the amping coefficient accoringly was propose by Tsumugiwa et al. [7]. Most of these methos along with others [8], [9] use the minimum jerk trajectory moel [1], which suggests that the human arm moves with minimal acceleration uring a point-topoint linear motion. However, this moel requires a priori knowlege of the movement, that restricts the usage of these methos in unstructure tasks. Summarizing, there are ifferent approaches to implement variable amittance control in orer to achieve effective interaction, which share the basic iea; the moification of the amping coefficient base either on monitore variables or optimisation criteria. On the one han, by monitoring variables such as the velocity or the applie force by the human no optimal solution is guarantee since the propose algorithms are erive in a heuristic way. On the other han, these optimisation techniques are task epenent an cannot be easily extene to other motion profiles. In this paper, a metho to combine human knowlege with a learning metho is introuce for an optimal variable amittance control scheme. To emulate the human ecision making process an on-line Fuzzy Inference System (FIS) is propose that etermines the esire amping of the amittance controller using only the joint position sensors of the robot an an external force sensor. In orer to tune the FIS for optimal cooperation a Fuzzy Moel Reference Learning Controller (FMRLC) is use for aapting the FIS towars the minimum jerk trajectory moel. Although explicit knowlege is require for the FMRLC training proceure, the traine FIS presents better performance than the heuristically tune FIS even in unknown motion profiles. The propose system is evaluate on an experimental set-up of a linear point-topoint motion using a KUKA LWR robot an the performance is measure with a number of subjects in terms of the require effort an the overall completion time.

2 II. ADMITTANCE CONTROLLER In phri amittance control is mainly use because it can establish a ynamic relationship between the forces/torques applie to the robot an the isplacement/velocity. In a human-robot cooperation task that is investigate here, the human acts as the leaer an efines the motion, while the robot is the follower an must comply to the applie forces by the human. The amittance controller of the robot is escribe by a typical secon-orer relationship: m e + c e = F h (1) where e = ref is the eviation of the actual velocity from the reference velocity ref =, m is the virtual inertia an c the virtual amping. The virtual stiffness k is set equal to zero since no restoring force is esire. The operator by applying a force F h, which is the input to the amittance, perceives a mass m in a viscous environment c. The virtual inertia has a negligible effect on the cooperation although it is suggeste that it shoul be ajuste proportionally to the amping for stability issues [5]. Furthermore, the lower limits of the amittance parameters have to be efine to avoi unstable behaviour [11]. Before the parameter upate law is evelope, the cooperative motion is stuie. A. Cooperative Motion In orer to select the optimum parameters of the variable amittance controller the point-to-point movement of the human alone an then in cooperation with a robot is investigate. In both cases the motion follows the minimum jerk trajectory in a straight line [1] an can be ivie into two phases; a rapi movement with low accuracy for approaching the target an a high accuracy movement with lower velocity for accurate positioning [12]. In a leaerfollower cooperation between two humans a blinfole follower that oes not have knowlege about the target constantly aapts the impeance characteristics of his/her arm by following the same trajectory. The minimum jerk trajectory minimizes the change in acceleration of the movement of the human han an it is expresse by the following objective function: M = tf... x 2 t (2) where t f is the uration of motion. Assuming that the velocity at the beginning an en of the movement is zero (ẋ = ẋ tf = ) an that the movement takes place along a straight axis, the position as a function of time is: x(t) = x + (x f x )(6τ 5 15τ 4 + 1τ 3 ) (3) where τ = t/t f, τ 1 an x, x f are the initial an final positions respectively. From Eq. (3) the velocity of the minimum jerk moel can be calculate through numeric ifferentiation. By monitoring the measure velocity uring the cooperation an by aapting the amittance controller to the minimum jerk trajectory a human-like performance can be achieve. With large amping large force is require by the human but it is easier to perform high accuracy movements since the robot motion is smoother. On the other han, low amping reuces the human effort in the expense of less accurate movements. In a point-to-point motion, the rapi movement phase woul benefit from a low amping while a higher amping woul assist the human in more accurate positioning. This observation raises the nee for on-line ajustment of the amping parameter to enable both effortless motion an high precision. B. Fuzzy ariable Amittance For the evelopment of low complexity an low cost robot assistants, the robots shoul use information from a minimum number of sensors with low computational cost, so computer vision techniques with visual cues are exclue. For the minimum jerk moel explicit knowlege of the motion is require which is not efficient for arbitrary tasks. Therefore, we wish to combine expert knowlege with a learning algorithm for efficient human-robot cooperation on arbitrary point-to-point movements. Fuzzy logic is a very effective tool to represent expert knowlege with linguistic rules an create a human-like inference mechanism. Examples of fuzzy logic an impeance control can be seen in rehabilitation robotics [13] where a fuzzy inference system was implemente to ajust the controller parameters accoring to the patient s arm impeance. In this paper an on-line fuzzy variable amittance control scheme is propose that aapts on-line the amping coefficient. A point-to-point movement is selecte on a single irection of the Cartesian workspace of the robot, as it is shown in Fig. 1. To minimise the cost an complexity of the propose metho only the joint position encoers of a robot are use along with a force/torque sensor at the eneffector. The propose FIS is a stanar fuzzy system [14] consisting of two inputs, the measure Cartesian velocity along a single irection an the corresponing force F h along the same irection. The output of the FIS is the virtual amping c of the robot amittance controller. For each input an output five triangular type membership functions are selecte that are uniformly sprea aroun zero. The selecte rules form a complete an consistent rule base meaning that for every possible inputs there are vali conclusions. The x x f + + y x Fig. 1: Experimental set-up.

3 initial rule base for the FIS, that is shown in Tab. I, can be interprete by the following sentences: IF Force is high (-2 or +2) AND elocity is high (-2 or +2) THEN Damping is very low (1). IF Force is zero () AND elocity is zero () THEN Damping is very high (5). IF Force is positive small (+1) AND elocity is negative small (-1) THEN Damping is very high (5). This initial rule base of the FIS is create in a heuristic manner. The selecte rules reuce the amping when the velocity an force F h are high, to facilitate the rapi movements an increase the amping at lower velocities for smoother positioning. Alternatively, an arbitrary rule-base is create by assuming that there is no knowlege about the control of the plant. A comparison within these two alternatives is conucte in section I. C. Stability Consierations In phri the human uses haptic an visual feeback from the plant to regulate his/her action. Therefore, the human is part of the controller an is very ifficult to moel an prove the overall stability of the system. Experimental stuies on impeance control [15] showe that the robot coul present unstable behaviour with very low virtual amping, high virtual inertia or stiff environment. It is suggeste that the human arm has a maximum impeance [16], that occurs when the human stiffens his arm. To guarantee the stability of the propose system, the lowest value of c crit is experimentally foun equal to 1N s/m, given a value for m = 1kg an high stiffness of the operator s arm. III. FUZZY MODEL REFERENCE LEARNING CONTROLLER In this section a learning system is evelope in orer to improve the performance of the heuristically create FIS in section II. A Fuzzy Moel Reference Learning Controller (FMRLC) is propose that combines feeback information from the plant an a reference moel in orer to aapt the FIS system [14]. The FMRLC loop consists of the reference moel, the fuzzy inverse moel an the aaptation mechanism which is the knowlege-base moifier of the FIS, as it is illustrate in the block iagram of Fig. 2. The minimum jerk moel of Eq. (3) is use as reference for aapting the FIS knowlege-base so as to perform similarly to a blinfole human assistant that relies only on haptic information. During the cooperation, the error y e between TABLE I: Manually tune initial FIS rule-base. F h C the actual measure velocity an the minimum jerk moel velocity jerk is calculate as: y e = jerk (4) an is passe to the Fuzzy Inverse Moel (FIM). The FIM characterises the inverse function of the cooperation, has only one input an etermines a value p that is use by the knowlege-base moifier to reuce the error y e. Each input/output of the FIM consists of five triangular shape membership functions evenly istribute aroun zero. Since the value y e is the error between the velocities, the rules of the inverse moel of the cooperation have the following form: IF y e is zero THEN p is zero. IF y e is positive THEN p is negative. IF y e is negative THEN p is positive. The knowlege-base moifier aapts the FIS by ajusting the centres b m of the output membership functions that are associate with the rules responsible for the previous controller action ref (kt T ). T is the sampling perio in the iscrete time omain. The centres of the FIS output membership functions are then upate accoring to the following equation: b m (kt ) = b m (kt T )+pµ m (F h (kt T ), (kt T )) (5) This upate formula shifts the centres b m (kt T ) by the amount p an in proportion to the certainty of the premise µ m (F h (kt T ), (kt T )), µ m 1. In that way, the output membership functions with higher premise certainty are tune at a larger amount because they have greater impact in the output c of the FIS. For example, if the actual velocity uring the cooperation at time kt is lower than the optimal minimum jerk velocity jerk, then y e > an p <. The knowlege-base moifier reuces the centres b m accoring to Eq. (5) an the FIS prouces a lower amping for the amittance controller, enabling the operator to move at a higher velocity with less effort. Such an aaptation algorithm creates an input-output mapping to the FIS between the velocity, force F h an amping c that facilitates the cooperation accoring to the minimum jerk trajectory moel. jerk Min. Jerk Moel τ Human F h Knowlege-base p moifier Δb m Fuzzy Inference System c Amittance Controller Fuzzy Inverse Moel ref y e Robot Training loop + - Fig. 2: Block iagram of the propose fuzzy moel reference learning variable amittance controller. The ashe line represents the proprioceptive visual an haptic feeback of the human operator.

4 To avoi unstable behaviour, the centres of the FIS must not rop below the critical amping value c crit. To ensure stability an the safety of the operator the following latching criterion is ae that restrains the minimum amping above = 1Ns/m: c crit If b m (kt ) < c crit T hen b m (kt ) = c crit (6) The training (FMRLC) loop operates at the same frequency as the amittance control loop an the overall pointto-point motion is iterate a number of times until the metho converges. After the training is complete, the FMRLC loop is no longer require, since the traine FIS has aapte to infer the optimal amping coefficient for cooperation. Although the selection of both the FIS an the FIM is conucte in a heuristic way, the traine FIS contains the association between the velocity, the force an the virtual amping aapte to the minimum jerk moel rather than an association between the position an the amping. As a result, the FIS is not relate explicitly to the minimum jerk moel an it can be scale to ifferent movements as it is shown in section I-B. I. EXPERIMENTAL EALUATION The evaluation of the propose variable amittance control scheme is conucte in two stages. The first stage inclues the training process, where the FIS is aapte to the minimum jerk trajectory using the FMRLC an in the secon stage the traine FIS is teste into ifferent movements. The experimental set-up consists of a KUKA LWR I robot with a force/torque sensor mounte at the en effector, as it is shown in Fig. 1. The human cooperates with the robot in a single irection of the Cartesian workspace using the hanle. The force sensor measures the force F h applie by the human, which is the input to the variable amittance controller. The output velocity of the amittance controller ref is translate into reference joint velocities q ref using the inverse Jacobian matrix: q ref = J 1 (q) ref (7) Since the reunant joint of the robot is not use, J(q) is the 6x6 Jacobian matrix, q ref a 6 element vector an ref = [ ref ] T for motion into axis x of robot base Cartesian coorinates. Each joint incorporates an internal position controller an the reference velocity q ref is erive through incremental position commans: q(kt ) = q ref (kt )T + q(kt T ) (8) where T =.1s is the sampling perio of the amittance control loop. A. FMRLC Training To train the FIS into the minimum jerk moel of Eq. (3), the initial x an final x f position as long as the require time of the motion t f have to be specifie. In orer to measure the time t f, five subjects are recore iniviually (without cooperating with another human or robot) uring a linear constraine point-to-point motion with visible initial x an final x f positions. During the movement each subject hols a mass equal to m = 1kg which is equal to the virtual mass use in the amittance controller later. After multiple iterations it is foun that for a istance of.3 metres the mean time t f for an iniviual human to complete the minimum jerk trajectory is 1.3 secons with a stanar eviation of.19 secons. The same movement is then conucte by a human in cooperation with the robot for the aaptation process. The human is aske to move the robot from the initial position x = m to the target x f =.3m. A laser pointer attache to the hanle projects the position of the robot to the groun where the initial an the target points are visually marke in orer to assist the human with visual feeback. During the movement the FIS constantly calculates a corresponing amping accoring to the current velocity an force. The FMRLC measures the eviation y e from the minimum jerk trajectory, which is known for the specific movement an aapts the FIS accoring to the knowlege-base moifier. The movement is repeate 1 times by a human an it is observe that the error y e converges towars zero. To evaluate the performance of the propose aaptation metho three ifferent scenarios are investigate involving human-robot cooperation in a point-to-point motion. For each scenario the actual velocity of the human-robot system over time τ is compare with the theoretical minimum jerk moel velocity jerk as it is illustrate in Fig. 3. Specifically, in Fig. 3a the manually tune FIS without the aaptation mechanism is investigate an the corresponing surface of the fuzzy system is illustrate. It is clear that the heuristic tuning of the FIS is insufficient for optimal results, since the mean velocity profile iffers significantly from the minimum jerk moel an the root mean square error (RMSE) is quite high (Tab. II). On the contrary, the FMRLC aaptation with the initial rule-base of Tab. I (shown in Fig. 3b) emonstrates very close approximation of the velocities to the optimal moel an has the smallest RMSE. Finally, in Fig. 3c an arbitrary initial rule-base for the FIS is selecte with the initial centres of all output membership functions being b m = 55, m = 1, 2,..., 25. Although, the initial FIS oes not contain any knowlege about the plant, the mean velocity approaches the minimum jerk moel at a large percentage with a small RMSE. By comparing the surfaces of the resulte FIS it can TABLE II: The root mean square error (RMSE) between the actual velocity an theoretical minimum jerk velocity, the mean values an stanar eviation for the energy an completion time for the three ifferent scenarios. Metho RMSE Energy (J) Time (s) mean st mean st Untraine FIS FMRLC with manual FIS FMRLC with arbitrary FIS

5 .5 (a).5 (b).5 (c) τ τ τ c F c F 5 Fig. 3: Experimental results using (a) the untraine, (b) the traine FIS (FMRLC) with initial expert knowlege of Tab. I an (c) the traine FIS of the arbitrary initial knowlege-base. In the top row the mean measure velocities an the stanar eviations (continuous lines with vertical bars) are overlai on the optimum minimum jerk trajectories (ashe lines). In the bottom row are illustrate the input-output surfaces of the use FIS..2.2 c F be conclue that the rules with the most impact on the performance of the overall system, inclue the cases where both the velocity an the force F have the same irection (symmetric on positive an negative irection) an large values. For example, the surface of the arbitrary initial rulebase (Fig. 3c) has similar appearance to the manually tune rule-base in the ranges aroun F = 5N an =.2m/s (Fig. 3a). In such large values the esire amping shoul be as low as possible in orer to assist the human. As it is epicte in the surfaces of Fig. 3a an Fig. 3c the FMRLC successfully aapts the variable amittance controller in the optimal values. Between surfaces (a) an (b), although ifferences are not very obvious, there is an improvement of the FMRLC over the manually tune FIS as it is shown in Tab. II. The mean energy transferre by the human to the robot an the mean time require for completing the movement appear to be lower for the FMRLC with the initial rule base of Tab. I. The FMRLC with the arbitrary initial rule base requires the most effort for the human although the time require is similar to the untraine FIS. Summarizing the results, the combination of the human knowlege an the FMRLC aaptation algorithm presents the best performance in terms of human effort an completion time. B. Testing To valiate the results of the traine FMRLC aaptation algorithm, the traine FIS with the initial rule base of Tab. I is teste against the untraine, manually tune FIS into ifferent movements that are unknown to the robot. The movements are performe by 12 subjects age from 24 to 42 years ol, ten of them male, two female an all right hane. One of the subjects participate in the training proceure an ten of them have never interacte with the robot before. Each subject is aske to grab the robot hanle from the starting position, guie it to a target position, rest in that position for a secon an guie it back to the starting position for a total of 1 point-to-point movements. A laser pointer in the hanle projects a re ot in a white surface with marke targets in front of the subjects assisting them with visual feeback. For each subject, three ifferent movements are conucte with istances x f =.2m,.3m,.4m an each movement is repeate for the traine FIS of Fig. 3b an the untraine FIS of Fig. 3a. To reuce the effects of the human learning through the process, half of the subjects are initially teste to the traine FIS, while the other half are teste to the untraine FIS first. The subjects are aske to complete every movement with the velocity an precision they prefer. For a total number of 72 movements, the applie forces an the corresponing velocities in the irection of motion are recore. In the first iterations of each movements it is observe that subjects without previous interaction with the robot move with a very small velocity until they become familiar with the robot operation. As a results, the first two iterations of each movement are not taken into consieration. The mean energy an elapse time of all subjects are illustrate in Fig. 4 for the three istances an the two ifferent FIS. As expecte, the energy provie by the human increases proportionally with the istance of the point-to- Energy (J) Mean energy Manual tune FIS FMRLC traine FIS Distance (m) Time (s) Mean time Distance (m) Fig. 4: Mean values an stanar eviation of energy an time from all subjects in three ifferent movements.

6 point movement. The mean energy require with the FMRLC traine FIS appears to be lower than the untraine FIS particularly in large movements. For x f =.2m there is a negligible improvement 1% in the effort with the FMRLC traine FIS, which increases at 7% for x f =.3m an finally at 13% for x f =.4m. These results suggest that for large isplacements subjects ten to apply larger forces an velocities which benefit from the FIS aapte to the minimum jerk moel. Moreover, the stanar eviation of the effort in the traine FIS is 38% lower than the untraine. Although the effort appears to increase proportionally to the istance of the movement, the require time oes not, mainly because in the first movements the subjects are overcautious on applying large forces. However, by comparing the two FIS it appears that in the traine FIS the mean time is lower than the untraine for a total average of 12%, since the FMRLC traine FIS facilitates the accurate positioning to the target through the optimal variable amping. It is observe that with the untraine FIS most subjects ten to overshoot the target an apply correcting movements that increase the overall time. With a questionnaire given to the subjects right after the experiment, they were aske to rate the two controllers in each of the three movements in terms of intuitiveness. The subjects were not aware of the type of each controller. The results liste in Tab. III show that in lowest isplacement of x f =.2m most subjects (58%) cannot istinguish the ifference between the controllers mainly because of the low velocities an forces. For x f =.3m, 42% prefer the FMRLC traine FIS while the rest 5% still are not able to istinguish any ifference. Finally, for the largest isplacement of x f =.4m all of the subjects coul istinguish between the two methos with 84% preferring the FMRLC traine FIS. In the overall experiment the FMRLC traine FIS is preferre over the untraine an the higher the isplacement the more evient the performance gain is to the subjects. TABLE III: Questionnaire results on the most intuitive controller. User selection x f =.2m x f =.3m x f =.4m Untraine FIS 8% 8% 16% FMRLC traine 34% 42% 84% No ifference 58% 5% %. CONCLUSIONS In this work a variable amittance control scheme is propose for human-robot cooperation that combines a humanlike inference mechanism with an aaptation algorithm for optimal tuning of the amping coefficient. Base on the velocity of the cooperation an the force applie by the operator, a heuristically create FIS infers an appropriate amping for the amittance controller, that assists both the rapi movements of the human an the accurate positioning. A moel-reference training proceure base on FMRLC aapts the manually tune initial knowlege-base of the FIS to the minimum jerk moel. It is observe that the initial knowlege-base of the FIS has a significant performance improvement in the cooperation in terms of the require effort of the human an the uration of the motion. Experimental results with multiple subjects suggest that the traine FIS enables a more intuitive interaction than the untraine, by reucing the effort an by assisting accurate positioning, even in ifferent movements that those use to aapt the controller. Future work on the propose control scheme involves the generalisation of the methos in arbitrary motion profiles by ecoupling the goal position from the controller. REFERENCES [1] N. Hogan, Impeance Control: An Approach to Manipulation, in 1984 American Control Conference, vol. 17, pp , IEEE, [2] R. Ikeura, H. Monen, an H. 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