Model and Modeless Friction Compensation: Application to a Defective Haptic Interface

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1 Model and Modeless Friction Compensation: Application to a Defective Haptic Interface Gianni Borghesan, Claudio Melchiorri Dipartimento di Elettronica, Informatica e Sistemistica Bologna, Italy {gianni.borghesan,claudio.melchiorri}@unibo.it Abstract. This paper describes a preliminary work devoted to the design of a control architecture for a defective haptic interface, i.e. an underactuated haptic interface not able to apply forces along arbitrary directions. This interface is intended to be used for grasping tasks, where unilateral constraints are usually present. The main control problems considered in this paper concern the study of friction compensation techniques by means of a force feedback loop and a feedforward controller. This has been implemented with three different methods: two are based on a model of the friction present in the actuation system, while the latter on a Momentum Observer. These schemes have been experimentally tested on a simplified setup of the haptic interface, composed by a linear motor, a force sensor, and a Kevlar wire. Two sets of experiments have been considered, i.e. free space motions and interaction with a virtual wall. Key words: Haptics, friction compensation, Momentum Observer, wirebased interfaces. 1 Introduction At the moment, very few haptic interfaces are available for grasping and manipulation purposes. Among the most known, one can mention the Rutgers Master II-ND Force Feedback Glove [1], the The Pure Form exoskeleton, [2,3], and the CyberGrasp by Immersion, [4], a commercially available system. These devices have to be worn on the hand of the user, and their design resemble a glove-like exoskeleton, endowed with small robotic devices that apply force feedback on three or more finger tips. These interfaces normally present a mechanism that balance their weight, such as a landed robot that provides also the kinestetic force feedback to the user wrist. The main drawback of exoskeletons is the operator uneasiness in wearing bulky devices, that can divert the attention from the task and disrupt the haptic illusion. Moreover, the free space movements are seldom realistic, both for the feeling of constriction on the user hand, and the augmented inertia of the whole structure. This work describes the preliminary study of a defective interface based on wires, designed in order to leave the user

2 2 Gianni Borghesan, Claudio Melchiorri hands free in a quite wide workspace. The basic idea is to use, for each fingertip, a wire connected, through a pulley to a load cell mounted on a linear actuator, as shown in Fig. 1. This particular mechanical design is motivated by the benefit of having a negligible inertia connected to the user. On the other hand, it introduces a limitation on the directions along which the haptic interface can display a force. In particular, a one-wire haptic interface is unable to render force in a arbitrary direction, but only in the traction axis, i.e. the direction connecting the user finger tip to the pulley. For this reason this device is said defective, as in [5], where other issues connected to the use of this kind of interface have been addressed. This work is devoted to the comparison of control schemes for friction compensation, tested with experiments on free space motions and virtual wall rendering. Since the current setup is not provided with position sensors able to retrieve the pitch and yaw angles of the wire, as planned for future developments, it is not possible to reconstruct the user position. For this reason, only a one DoF displacement is considered. This paper is structured as follows: Section 2 describes the experimental setup and the control architecture; Section 3 illustrates the proposed control schemes, that employ a force feedback control and a feedforward action, based on a static friction model (Subsec. 3.1), a dynamic friction model (Subsec. 3.2), and a Momentum Observer (Subsec. 3.3). Experimental results and final remarks are presented in Section 4 and Section 5, respectively. 2 Experimental Setup The final goal of this activity is the development of a haptic interface for grasping and manipulation tasks in virtual environments using up to five fingers. At the moment, with the goal of verifying the effectiveness of the design, an interface involving only two fingers, for pinch grasps and simple manipulations tasks, has been developed. It is based on two linear motors LinMot P1-23Sx8 with the servo controller LinMot E21-VF. The motors are equipped with position encoders with a resolution of 4 µm, and high sensitivity load cells are placed on the top of the motor sliders. The control is implemented on a Pentium IV PC equipped with a Sensoray 626 data acquisition board. The OS is RTAI-Linux based on a Debian distribution, with Linux kernel patched with RTAI 3.4. The real time I/O support for the acquisition board is provided by the Comedi drivers. The sample period for the digital controller and the D/A and D/A operations is 1 msec. The control design has been developed within the Matlab/Simulink and Real Time Workshop environments, while the experimental data have been monitored with xrtailab. Since this paper is focused on the control aspects only, and in particular on friction compensation methods able to improve the general behavior of the interface, the experiments illustrated in the following sections have been carried out using only one of the two motors. The schematic of the setup is shown in Fig. 1.

3 Model and Modeless Friction Compensation 3 Due to the necessity of modeling the friction effects, an identification procedure has been performed on the motor. In particular, the identified parameters are: the break-away or stiction force F b = 2N (the maximum force that can be exerted on the slider before any movement takes place); the Coulomb friction force F c = 1.7N (a constant force exerted by frictional phenomena when the slider moves); and the viscous friction, that results negligible F v N. The system is also affected by cogging forces (a position dependent force due to the permanent magnets of the slider) of approximately 1N, that have not been taken into account. Pulley Load Cell Slider Stator Fig. 1. Experimental setup. 3 Control Schemes The control schemes considered in this paper include a force feedback loop and a filter that rejects high frequency disturbances on the force sensor. In [6], the use of force feedback and friction compensation techniques for haptic interfaces is discussed. In particular, a Hybrid controller (a scheme including a force feedback with a variable gain and a smoothed Coulomb model) is proposed for obtaining high performances in free space. The control schemes presented in the following Subsections 3.1 and 3.2 are somehow inspired by the these results. An overview on classical friction models can be found in [7]. 3.1 Stick Slip model based friction compensation A quite common model for friction effects is the stick slip model [7], whose application to the control of haptic interfaces has been described in [8]. The

4 4 Gianni Borghesan, Claudio Melchiorri d dt Stick Slip Model f e Force Reference K f g f e Position Motor, Load Cell Fig.2. Control scheme based on Stick Slip friction model compensation. friction model is expressed by: { sgn(fu )min{ F u, F b }, v < v min f = (1) F c sgn(v), v v min where f is the estimated friction force, F u is the force applied -in our case- to the motor slider, F b is the break-away force constant, F c is the Coulomb force constant, v is the velocity, and ( v min, v min ) defines the dead zone (the state in which the stiction is the predominant friction phenomenon). This model is static, and needs as input the velocity v and the force F u acting on the motor slider (i.e. the sum of the reference force and of the force exerted by the user). Note that the gravity force f g must be compensated before feeding the force input to the friction model. The block diagram of this control scheme is reported Fig. 2, where in particular it is shown where the friction model (the block labeled as Stick Slip Model ) is inserted. 3.2 Dahl model based friction compensation This model is dynamic and needs only position/velocity measurements, so it is suitable also for systems in which the external forces are not explicitly known. The general formulation of the Dahl model is [9]: df dx = σ ( 1 df F c sgn(v) ) α (2) where σ is the so-called stiffness coefficient, and α defines the shape of the strainstress curve (in this paper, the value α = 1 is assumed). In [1], a discretized version of this scheme has been employed in an open loop friction compensation scheme for a telerobotic system. Since the system used in [1] was not equipped with force sensors, the friction compensation has been implemented with a feedforward action. Its formulation is: f i+1 = F c sgn(v i ) + (f i F c sgn(v i ))e σ Fc xi+1 xi (3)

5 Model and Modeless Friction Compensation 5 Dahl Model Force Reference K f g f e Position Motor, Load Cell Fig.3. Control scheme based on Dahl model friction compensation. d dt v Mass p ˆp ˆp f k L ˆf d Mom. Observer f k f c f e ˆf d Force Reference K f e Position Motor, Load Cell Fig.4. Control based on friction compensation by Momentum Observer. where sgn(v i ) is computed as: sgn(v i ) = sgn(x i+1 x i ) (4) Note that the model (3) is rate independent. The block scheme of Fig. 3 describes how this model is used in the control scheme. 3.3 Momentum Observer based friction compensation The goal of this control strategy is to compute the unmodeled forces, in this case the frictional forces, by means of a (linear) Momentum Observer, and then to feedforward to the actuation system a correction term so that the system behaves as a pure mass. This control scheme has been employed in [11], with

6 6 Gianni Borghesan, Claudio Melchiorri the aim of detecting and isolating actuator faults, and used in [12] where the problem of estimation and rejection of spurious forces acting on a linear drive was investigated. Let p = mv be the momentum of the motor slider, and ṗ its time derivative. Then: ṗ = m v = F = f k + f d (5) F is the sum of the forces acting on the motor slider and m the motor slider inertia. In particular, F takes into account two terms: f k, the known forces, in this case the control force f c and the external force f e measured by the load cell; f d, the unknown disturbance force. From (5), the momentum p can be estimated as: ˆp = (f k + ˆf d )dt (6) where the unknown term ˆf d can be computed by: [ ] ˆf d = L (f k + ˆf d )dt + p = L( ˆp + p) (7) where L is a positive coefficient. From (5) and (7), the following equation is obtained: ˆf d = L ˆf d + Lf d (8) This equation represents a linear filter with unitary gain, input f d, state ˆf d, and a bandwidth of L [rad/s], which final value converges to f d. From (6) and (7), the linear estimator is finally obtained: ˆp = f k + L(p ˆp) (9) ˆf d = L(p ˆp) (1) This estimator needs as input both the velocity v (in order to compute the momentum p) and the known force term f k. The most critical parameter of the observer is L, the bandwidth of the filter, that influences the settling time for the error e = p ˆp. This parameter is limited by the frequency of the position acquisition, that in turns influences the digital noise of the velocity estimation, as explained in [12]. In this paper the value L = 1 rad/s has been assumed. Fig. 4 shows how the observer is implemented within the control scheme. Note the saturation block, used to maintain the signal fed to the motor in the correct range. Otherwise, the AD/DA would saturate the force signal anyway, but in this case the input ˆf d and the force input fed to the motor would be different. Moreover, it is not necessary to compensate gravity explicitly, since its contribution is constant and it is automatically estimated and compensated by the observer.

7 Model and Modeless Friction Compensation 7 Fcell [N] Fcell [N] Fcell [N] Stick Slip Dahl Mom. Obs V elocity [m/s] Fig.5. Free Space experiment: feedforward friction compensation by Stick Slip model (top), Dahl model (middle), Momentum Observer (bottom). The time evolutions are counterclockwise. 4 Experimental Results In order to compare the different methods, some experimental tests, where the user explores the free space (Fig. 5) or a virtual wall (Figures 6(a) and 6(b)), have been performed. In all the tests the gain of the force control loop has been maintained constant (K = 8). 4.1 Free Space The free space experiment has been executed by moving the thimble back and forth, with a maximum velocity of approximately.4 m/s. A constant force of.4 N is applied by the motor on the thimble in order to maintain the wire tensioned. This force does not disturb the haptic illusion, and is the minimum force able to keep the wire stretched in the range of working conditions used in the experiment. Each experiment has a time length of 1s. The plots of Fig. 5 relate the force exerted on the load cell to the velocity, obtained via discrete differentiation of encoder position. The ideal behaviour would be a complete compensation of both friction and dynamical effects of the slider inertia, resulting in a constant force of.4n. The expected behaviour is a small error force for high velocities, and a critical zone near the null velocity, where hysteresis phenomena occur. By direct inspection of Fig. 5, it is possible to qualitatively characterize the influence of the different feedforward actions. The Stick-Slip and Dahl model present a difference between the positive and negative high velocities (roughly when v.15 m/s) of about.1n. This bias is generated by an asymmetric behavior of the motor respect to the movement direction. Close to null velocities, the Dahl model shows the lowest error, while the Stick-Slip model generates the

8 8 Gianni Borghesan, Claudio Melchiorri highest one. The difference between the reference force and the positive or the negative forces represents the effort needed to overcome the static friction. In the left portion of Fig. 6(a) (i.e. for position < 6mm), where position is reported as a function of the applied force (measured by the load cell), it is possible to see how the bias observed in Fig. 5 (with the controllers based on the Stick-Slip and Dahl models) create a position/force hysteresis phenomenon. In fact, while moving back and forth, the user feels different forces depending on the motion direction. On the other hand, the control scheme based on the Momentum Observer is able to keep the force roughly constant, as shown by the overlapping traces in the bottom plot of Fig. 6(a). 4.2 Virtual Wall The results obtained during the interaction with a virtual wall placed at a position p = 6 mm are now described. The stiffness of the virtual wall has been set to K = 3 N/m. Fig. 6(a) and Fig. 6(b) report the data acquired during the experiments using the three different control schemes, each one with a time length of 3 seconds. In Fig. 6(a) the load cell force is plotted as a function of the position, while in Fig. 6(b) the time evolution of the position is reported. The control based on the Stick-Slip model has an unstable behaviour while interacting with the virtual wall; this undesired response can be avoided by lowering the gain of the force loop, to the detriment of the free space performance. The controllers based on the Dahl model and the Momentum Observer present a stable behaviour; the response can be evaluated in Fig. 6(a). A simple criterion to compare the two models is to look, in Fig. 6(a), at the wideness of the cone departing from the point (F cell =.4 N, position = 6 mm), and at the number of oscillations needed to stabilise the system on the reference force, i.e. the line of slope K wall = 3 N/mm. The control based on the Momentum Observer shows a faster recovery time and a narrower cone. Another factor that can be used to evaluate the control schemes is the depth of penetration of the haptic interface in the virtual wall, reported in Fig. 6(b). From the analysis of the experimental data, in the authors judgement, the scheme with the Momentum Observer shows the best response. The free space experiment does not show asymmetry in the force/velocity relationship, thanks to the automatic correction capability of the Momentum Observer; moreover, the virtual wall experiment shows the fastest convergence to the reference force. It is also worth noticing that this scheme does not employs any model, and therefore no effort is needed for identification procedures. 5 Conclusions In this paper, three different control schemes, constituted by a force feedback loop and a feedforward action for friction compensation, have been employed

9 Model and Modeless Friction Compensation 9 Fcell [N] Fcell [N] Fcell [N] Dahl Stick Slip Mom. Obs position[mm] (a) Force Vs. Position pos.[mm] pos.[mm] pos.[mm] 6 55 Dahl Stick Slip Mom. Obs time [s] (b) Position Vs. Time Fig. 6. Virtual Wall experiment: friction compensation by Stick Slip model (top), Dahl model (middle), Momentum Observer (bottom). to control a one DoF defective wire haptic interface equipped with a force sensor. The friction compensation action is computed according to three different modalities: with a Stick-Slip or a Dahl friction model, and with a Momentum Observer. The experimental tests outline the benefits arising from the use of the Momentum Observer with respect to the other two methods. The combined use of a wire interface and of a control scheme able to compensate for the undesired dynamics allows the user to feel the motion in the free space in a realistic fashion, being the perceived inertia practically null, and the force due to wire pretension small, and with negligible variations. The same control schemes have been tested also in the case of stiff contact with a virtual wall, resulting in a stable interaction for two of the proposed

10 1 Gianni Borghesan, Claudio Melchiorri control schemes. As in the free space exploration, the control scheme based on the Momentum Observer proved to render the interaction with higher fidelity respect to the other proposed control schemes, since the virtual wall experiment presents smaller oscillations about the nominal force (Fig. 6(a)) and a smaller penetration in the wall (Fig. 6(b)). Future developments of the interface will concern technical solutions able to acquire the thimble position and the study of the force rendering fidelity in grasping actions, when two or more devices are coupled. References 1. M. Bouzit, G. Popescu, G. Burdea, and R. Boian, The rutgers master ii-nd force feedback glove, in HAPTICS 2: Proc. of the 1th Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems. Washington, DC, USA: IEEE Computer Society, 22, p A. Frisoli, F. Rocchi, S. Marcheschi, A. Dettori, F. Salsedo, and M. Bergamasco, A new force-feedback arm exoskeleton for haptic interaction in virtual environments, in Proc. World Haptics 5, A. Frisoli, G. Jansson, M. Bergamasco, and C. Loscos, Evaluation of the pureform haptic displays used for exploration of works of art at museums, in Proc. World Haptics 5, Cybergrasp exoskeleton: Groundbreaking haptic interface for the entire hand. [Online]. Available: grasp.php 5. C. Melchiorri, G. Vassura, and P. Arcara, What kind of haptic perception can we get with a one-wire interface? in Proc. IEEE ICRA 99, Detroit, Michigan, 1999, pp N. L. Bernstein, D. A. Lawrence, and L. Y. Pao, Friction modeling and compensation for haptic interfaces, in Proc. IEEE WHC 5. Washington, DC, USA: IEEE Computer Society, 25, pp H. Olsson, K. J. Åström, C. C. de Wit, M. Gäfvert, and P. Lischinsky, Friction models and friction compensation, European Journal of Control, D.-S. Kwon and K. Y. Woo, Control of the haptic interface with friction compesation and its performance evaluation, in Proc. IEEE IROS, Takamatsu, Japan, 2, pp P. Dahl, Solid friction damping of mechanical vibrations, AIAA Journal, vol. 14, no. 2, pp , M. Mahvash and A. M. Okamura, Friction compensation for a force-feedback telerobotic system, in Proc. IEEE ICRA 6, Orlando, Florida, 26, pp A. D. Luca and R. Mattone, Actuator failuture detection and isolation using generalized momenta, in Proc. IEEE International Conference on Robotics and Automation, Taipei, Taiwan, 23, pp G. Palli and C. Melchiorri, Non-model based friction and load compensation in linear electric drives, in Proc. 4th Int. Symp. on Motion Control, 27.