Analysis and Design of a Haptic Control System: Virtual Reality Approach

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  • Int J Adv Manuf Technol (2002) 19:743751Ownership and Copyright 2002 Springer-Verlag London Limited

    Analysis and Design of a Haptic Control System: Virtual RealityApproachM.-G. Her, K.-S. Hsu and W.-S. YuDepartment of Mechanical Engineering, Tatung University, 40 Chung-Sang North Road 3rd Sec, Taipei, Taiwan

    In this paper, the analysis and design of telerobotics based onthe haptic virtual reality (VR) approach for simulating the claycutting system is proposed. The main components of theapproach include a user interface, networking, simulation, anda robot control scheme. The telerobotics for the clay cuttingsystem and the environment is simulated by a haptic virtualsystem that enables operators to feel the actual force feedbackfrom the virtual environment just as they would from the realenvironment. The haptic virtual system integrates the dynamicsof the cutting tool and the virtual environment whereas thehandle actuator consists of the dynamics of the handle andthe operator on the physical side. The control scheme employsa dynamical controller which is designed considering both theforce and position that the operator imposes on the handleand feedforward to the cutting tool, and the environmentalforce imposed on the cutting tool and the feedback to thehandle. The stability robustness of the closed-loop system isanalysed based on the Nyquist stability criterion. It is shownthat the proposed control scheme guarantees global stabilityof the system, with the output of the cutting tool approachingthat of the handle when the ratios of the position and theforce are selected correctly. Experiments in the virtual environ-ment on cutting a virtual clay system are used to validate thetheoretical developments.

    Keywords: Clay cutting system; Haptic virtual system; x-ytype active handle

    1. Introduction

    Many industries (aviation, medicine, nuclear) employ remotedistant control systems for manufacturing in hazardous areassuch as nuclear sites, for training pilots with in-flight simu-lators, etc. [1] and latest experiences have shown that thesymbiosis of virtual reality (VR) techniques can work satisfac-

    Correspondence and offprint requests to: M.-G. Her, Departmentof Mechanical Engineering, Tatung University, 40 Chung-SangNorth Road 3rd Sec, Taipei, 10451 Taiwan. E-mail: d8601002mail.ttu.edu.tw

    torily. VR with a haptic property offers the chance to buildsimulation models for the operator for controlling the remotesystems. The interaction between the operators and teleroboticsfor remote and distant control processes is achieved byemploying some specified telemechanism that can copy humanactions at the end effector to carry out a task and vice versa[24]. An example of such processes is telerobotic systems ina virtual environment with a haptic property, which is of greatuse in environments where direct operator contact is deemedto be lethal or risky and the operator cannot keep watch onthe distant end-effector. The telerobotics and the environmentare simulated by the haptic virtual system that enables theoperator to feel the actual force feedback from the virtualenvironment just as she/he would from the real environment.The reaction forces from the virtual environment are felt bythe operator through a feedback control scheme. This allowsoperators to be located in a safe area and to control the distantmanipulator with a virtual image and duplicate on-line themotion of the distant processes quickly and accurately, so thatthey can feel the actual environment or the conditions ofoperation. However, it is well known that operator adaptabilityto the environment and to the conditions of operation is vitalfor a smooth operation. One way to cope with the problem isto let the operator intervene in the system from a safe distanceby means of a controller, and to be part of the overall closed-loop control system. Takahashi and Ogata [5] studied theteleoperation and humanmachine interfaces and simulated arobotic system using VR technology. In general, robot manipu-lators have been used by the manufacturing industries forperforming certain automation tasks, or used as a master/slavetype manipulator in teleoperation. They require an accuratemodel description for designing the stabilising controllers. Inparticular, hand controllers for creating various forces havebeen designed for manoeuvring the remote side of the slavemanipulator [6]. However, by this approach it is difficult toobtain the respective ratios of the position/position andforce/force between the master manipulator and the slave.Hirata and Sato [7] and Lee et al. [8] realised the teleoperationof a VR system with haptic characteristics that allows anoperator to probe and feel a remote virtual environment. It isseen that the performance can be improved significantly byproviding force feedback information from the remote site of

  • 744 M.-G. Her et al.

    the virtual environment to the master. The operator can applyforce by a powered handle to manoeuvre the system at theremote site to achieve a specific task. Satoshi and Hidetomo[9] developed a model for haptic behaviour which can giveoperators the feel that they are manoeuvring a mass, or pushingonto a spring or a damper. Minsky and Ouh-young [10]proposed a dynamic simulation to create virtual textures by apowered joystick system with force feedback devices. Forcedisplay is widely used in developing VR systems [11]. Liand Wang [12] modelled force/torque sensing for a workingenvironment using physical based components (e.g. mass andspring/damper) in the VR simulating system. However, an in-depth study of system stability analysis and the implementationof stabilising controllers in a VR system are still lacking.

    This paper presents telepresence/telerobotics with a hapticproperty based on virtual reality for simulating a clay cuttingsystem. The telerobotics and the environment for the cuttingtool system are simulated by the haptic virtual system whichenables operators to feel the actual force feedback from thevirtual environment just as they would from the real environ-ment. The main components of the haptic virtual system includea user interface, networking, simulation, and a robot controlscheme. In order to provide interaction between a human beingand a haptic virtual system, an x-y type active handle with aforce feedback sensor is required. The active handle is poweractuated and provides the force feedback to the operator. Thehaptic virtual system is the integration of the dynamics of thecutting tool and the environment, and the simulating systems,including the dynamics of the cutting tool actuator and theenvironment of the closed-loop control system. The controlscheme employs a dynamical controller which is designedconsidering both the force and position that the operatorimposes on the handle and the feedforward to the cutting tool,and the force from the environment imposed on the cuttingtool and the feedback to the handle. The stability condition ofthe closed-loop system is derived based on the Nyquist stabilitycriterion. The performance of the proposed control scheme isevaluated experimentally. The results of a series of experimentsperformed on cutting a virtual clay system are presented inthis paper to show the effect of the control scheme on thesystem performance and stability. It was shown that the virtualexperimental and the theoretical results are in good agreement,and that the designed controller is robust in a constrained/unconstrained environment.

    2. The Haptic VR Simulation System

    A VR system shown in Fig. 1 was developed to simulate thetelepresence of the clay cutting system with haptic properties.A block diagram of the system is shown in Fig. 2. Since theclay cutting system is usually manual, it is time consuming totrain a new operator, and irrecoverable errors often take placeduring the training processes. Therefore, it is proposed tosimulate the process with the haptic VR system for safety andeconomic reasons.

    The telepresence with a haptic property consists of a two-degree-of-freedom x-y type active handle and a computer inter-

    Fig. 1. A haptic VR system with x-y type active handle: experi-mental setup.

    Fig. 2. The diagram of the VR system with both physical and virtualsides.

    face which simulates the dynamics of the clay cutting systemand the environment.

    fh = uh Thyh (1)yh = Ghvh + Shfh (2)

    where yh, uh, and fh and respectively, are the handle position,the force imposed on the force sensor supplied by the operatorarm, the force imposed on the handle actuator and the feedfor-ward to the virtual side of the system. Gh is the transferfunction of the active handle actuator, and Sh is the transferfunction from fh to yh. For the virtual side, we have

    ft = ut Ttyt (3)yt = Gtyt + Stft (4)

    where yt, ut, and ft, respectively, are the cutting tool position,the environment force, the force imposed on the cutting toolactuator and the feedback to the physical side of the system.Gt is the transfer function of the virtual cutting tool actuator,and St is the transfer function from ft to yt. The transferfunctions Sh and St can be regarded as the stiffness of thehandle and that of the virtual cutting tool, respectively. It is

  • Analysis and Design of a Haptic Control System 745

    assumed that the actual system and the working environmentexpressed in the VR system can be approximated for modellingpurposes by using a spring and damper. Therefore, thedynamics of the cutting tool actuator with the environment ofthe VR system can be taken as:

    Gt = 1/Mts2 + Bts + Kt (5)where Mt, Bt, and Kt are, respectively, the virtual cutting toolmass, the coefficient of viscous damping, and the stiffness ofthe spring which is related to the modulus of elasticity of thematerial. The cutting tool actuator can drive the tool back andforth and to the desired position that the human operator wantsby controlling the handle.

    Since there are cross-feedback positions and forces betweenthe physical and virtual sides, the operator can feel the reactionforce between the cutting tool and the virtual clay system. Thecontrol procedures are monitored with the user interface inreal-time when the operators use the x-y type active handle tocontrol the cutting tool in the haptic VR system just as if theyare interacting with the real environment. Hence, by properlyselecting the compensators Ch1, Ch2, Ct1, and Ct2, the operatorcan feel the amount of necessary feedback force and move thehandle appropriately toward the desired position during thecutting process. The compensators work as a compliant controlfor the handle and the virtual cutting tool. Smaller compensatorgains increase stiffness of the handle and cutting tool. Wecannot choose Ch1, Ch2, Ct1, and Ct2 with very much largermagnitudes because the stability of the closed-loop system maybe compromised. In what follows, we first derive the relation-ship of the output positions of the handle and the cutting toolin the system.

    From Fig. 2, the control signals of the handle and the cuttingtool actuators can be obtained as

    yh = Ch1fh Ct1ft (6)vt = Ch2fh + Ct2ft (7)

    respectively.Hence, the respective outputs of the positions for the handle

    and the cutting tool can be given by

    yh = Gh(Ch1fh Ct1ft) + Shfh (8)yt = Gt( Chfh + Ct2ft) + Stft (9)

    A matrix Ah1 exists such that the following are satisfied:

    GtCh2 = Ah1(GhCh1 + Sh) (10)GtCt2 + St = Ah1( GhCt1) (11)

    Hence, we have from Eqs (10) and (11)yt = Ah1yh (12)

    where the elements of the diagonal matrix Ah1 denote the ratiosof the positions between the handle and the cutting tool in thex- and y-directions, respectively, and this is taken as theidentity matrix so that the handle and the cutting tool movethe same distance in the x- and y-directions, respectively.

    Thus, from Eq. (12), the positions of the handle and thecutting tool can influence each other with a one to one ratioby virtue of the haptic property.

    Next, we will derive the net force that the operator imposeson the cutting tool via the position of the handle to achieve acompliant control property. First, it is assumed that there isno external force from the environment, i.e. ut = 0 and thisleads to

    yh = Gh( Ct1 (I + TtGtCt2 + StTt)1 (TtGtCh2) (13)+ Ch1)fh + Shfh

    Then, suppose that the virtual side does not exist, i.e. the forceis imposed only on the handle by the human operator. There-fore, the handle position can be obtained by

    yh = GhCh1f 0h + Shf 0h (14)where f 0h is the force imposed on the handle actuator, as thevirtual side does not exist.

    However, it is seen that the net force, f eh, that moves thecutting tool purely on the virtual side can be defined by

    f eh = fh f 0h (15)From Eqs (14) and (15) this leads to

    yh = GhCh1(fh f eh) + Sh(fh f eh) (16)Then, manoeuvring the handle with the same trajectory, withand without considering virtual environment, we have fromEqs (13) and (16)

    f eh = (GhCh1 + Sh)1Gefh (17)where

    Ge = GhCt1(I + TtGtCt2 + ShTr)1 (TtGtCh2) (18)Furthermore, the relationship between ft and fh can be directlyobtained from Fig. 2 as follows:

    ft = (I + TtGtCt2 + ShTt)1 (GtTtCh2)ft (19)From Eqs (17)(19), we have

    ft = (Ct1Gh)1 (Ch1Gh + Sh)f eh = Ah2f eh (20)where the elements of the diagonal matrix Ah2 denote therespective ratios of the forces between the handle and thecutting tool in the x- and y-directions.

    Note that the force f eh is identical to ft if the matrix Ah2 ischosen as an identity matrix. This guarantees that the operatorcan feel the same amount of reaction force when the cuttingtool is cutting the oil clay system. Thus, the forces on thehandle and the cutting tool can influence each other at a ratioof one to one by the virtue of haptic property. If Ah2 and Ch1are selected properly, Ct1 can be obtained from Eq. (20) as:

    Ct1 = (GhCh1 + Sh) (GhAh2)1 (21)Similarly, using Eqs (10) and (11), Ch2 and Ct2 and aregiven by:

    Ch2 = ( Gt)1 Ah1(GhCh1 + Sh) (22)Ct2 = G1t (Ah1A1h2(GhCh1 + Sh) St) (23)

    respectively.Hence, we should select the compensators Ch1, Ch2. Ct1 and

    Ct2 properly such that the closed-loop VR system is guaranteedto be stable. In this paper, a sufficient stability condition will

  • 746 M.-G. Her et al.

    be derived using the Nyquist theorem for the closed-loopsystem when taking the operator and the environmentaldynamics into consideration in the closed-loop control system.

    3. Stability Analysis

    Since the motion of the x-y type active handle and the cuttingtool are independent in the x- and y-directions, respectively,we can let Gh = diag{Ghx, Ghy}, Gt = diag{Gtx, Gty}, Sh =diag{Shx, Shy}, St = diag{Stx, Sty}, Th = diag{Thx, Thy}, Tt =diag{Ttx, Tty}, and

    C1 = C2 = Ch1 Ct1Ch2 Ct2It is seen that the output y of the VR system is given by thefollowing compact form Fig. 3:

    y = (I + RGC + RS)1 (GC + S)u = Pu (24)It is seen that if P is a proper rational matrix and I + RGC+ RS 0, (0, ), then the closed-loop VR system isstable. Note that the stability condition does not give anyindication of the system performance but ensures only thestability of the system. Also the stability condition is only asufficient...

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