7-DOF Haptic device and interface design

Transcription

1 Turkis Journal of Electrical Engineering & Computer Sciences ttp:// journals. tubitak. gov. tr/ elektrik/ Researc Article Turk J Elec Eng & Comp Sci (2013) 21: c TÜBİTA doi:10.36/elk DO Haptic device and interface design Özgür BAŞER, Eran İlan ONUSEVEN Department of Mecanical Engineering, Middle East Tecnical University, Ankara, Turkey Received: Accepted: Publised Online: Printed: Abstract: In tis study, te developed 7DO aptic device (HaP7) and its virtual reality interface are presented. Te design issues, design constraints, and alternative design configurations are discussed and te potential advantages of te HaP7 are put forward. Te kinematic model of te proposed device looks like a simplified uman arm kinematic model. Te redundant caracteristic of te device provides larger workspace and allows for appropriate posture selection for te purposes of maimization of te rigidity, transparency and stability, wile minimizing te inertia and power consumption in addition to te singularity and obstacle avoidance optimization. ey words: Haptic device design, virtual reality, force feedback, visual feedback 1. Introduction Haptic devices are used to provide 3 or 6dimensional (3D/6D) data transfer between te users and computers in virtual reality (VR) applications [1]. Tey enable te users to touc te models designed in te virtual environment. Haptic devices sense te motion and force applied to te virtual objects by te user in its workspace and produce force feedback to te user. Te force feedback is computed based on te virtual models [2]. Due to te force feedback capability, VR applications are widely used in te areas of engineering, medical operations, teleoperation, welfare, and entertainment troug te development of computers and robotic tecnology [3]. Te most basic parameter in aptic device design is te number of degrees of freedom (DO). A aptic device can include one or more degrees of freedom. At least 3 DO are required to produce 3D force feedback. Since some VR applications need 3D torque feedback, a aptic device must ave 6 or more DO to reflect all of te 3D force and 3D torque feedback. Higer degrees of freedom may increase te area of applications and improve te performance of te aptic devices. In tis study, apart from te eisting commercial 6DO devices, a 7DO redundant aptic device is designed and its grapical user interface and implementation are presented. 2. Haptic devices in literature Tere are 3 types of design configurations in te literature: levitation aptic devices [4,5]. mecanical arm, cable driven, and magnetic In order to simulate te virtual models effectively, for te aptic devices it is desired tat te working volume, end point force/torque, rigidity, and resolution be maimized wile te backdrive friction, apparent mass, and backlas be minimized. Tese are considered as design parameters for aptic devices. Correspondence: konuk@metu.edu.tr 493

2 BAŞER and ONUSEVEN/Turk J Elec Eng & Comp Sci All of te required caracteristics mentioned above can be acieved by optimizing te design parameters of te mecanical arm aptic device. Utilization of cablecapstan drive mecanisms is generally preferred between te actuators and links to cancel te mecanical backlas in tis type of device [6]. In te cabledriven devices, te aptic andle is connected to te actuators by te cables directly. Tey cannot provide ig force/torque due to te cable weakness and large workspace due to te cable interference. Since vibration andicaps occur during operation, tey do not ave ig sensitivity. Even toug magnetic levitation devices ave ig sensitivity, tey ave quite a small workspace due to teir design concepts. Wen te potential designs are compared, it can be concluded tat te most suitable configuration is te mecanical arm design. In tis study, te design of te device is based on te mecanical arm configuration, including cablecapstan mecanisms. 3. Design and superiority of HaP7 Te mecanical arm device can be considered as a robot manipulator. A manipulator configuration can be purely serial or parallel mecanisms. Even toug te parallel structures ave ig stiffness and teir positioning accuracy is quite ig, serial manipulators ave larger workspace tan te parallel mecanisms. Te advantages of tese mecanisms can be incorporated by combining tem in one configuration, wic is called a ybrid mecanism [2]. In tis study, a ybrid type of configuration is used for te 7DO aptic device (HaP7) design (igure 1). In te design, 2 separate 3DO serial linkages eist at te base and at te tip of te device. Tese 2 serial configurations are connected to eac oter by 1 parallelogram. In order to minimize te apparent mass of te device, te static balance is performed for all moving parts, ecluding te aptic andle. or tis purpose, te fourt motor is used as a counterweigt so tat te static balance is acieved witout increasing te inertia (igure 1). Motor & encoder (3) Motor & encoder (4) (d 3 ) Motor & encoder (2) (d 4 ) Minimotor & miniencoder (1) orce/torque transducer Motor & encoder (1) Minimotor & miniencoder (2) Minimotor & miniencoder (3) igure 1. HaP7 and its kinematic model. Since te HaP7 as a redundant joint, it enables an approimate 20% increase in te workspace witout compromising te oter design criteria [4,5]. Moreover, te redundancy enables it to reac any point wit different postures in te workspace. Tis capability can be used to improve te performance. Te optimal posture can be selected for any target performance using te appropriate optimization tecniques. Tese targets 494

3 BAŞER and ONUSEVEN/Turk J Elec Eng & Comp Sci can be maimization of te stiffness, transparency, stability, minimization of te inertia, power consumption, singularity, or obstacle avoidance. Eac target can be considered as te superiority of te HaP7. Te redundant manipulators may reflect different stiffness caracteristics based on te selected posture due to te fleibility of te links and joints. Te most appropriate posture sould be selected for te ig precision applications. or tis purpose, te nonlinear least square optimization can be applied to find te appropriate redundant joint angle value by minimizing te end point deflection of te HaP7. Te cost function of te problem can be represented in terms of applied force, Jacobian matri J, and diagonal joint stiffness matri θ = Diag [ θ1, θ2,..., θ7 ]: ind θ redundant to minimize te total driving torques f (θ redundant ) = J T θ J 1. Recently, te performances of aptic devices are preferred for evaluation by means of teir transparency [7]. Te optimal posture can be selected in order to increase te transparency of te device. Optimal optimization selection enables te minimization of te parasitic forces coming from te dynamic and gravitational effects of te device. Te cost function of te problem can be represented in terms of mass matri M, centrifugal Coriolis matri C, gravitation matri G, and joint variables q : ind θ redundant to minimize te parasitic forces f (θ redundant ), f (θ redundant ) = M (q) q C (q, q) q G (q). Power minimization can also be acieved via optimum posture control for te HaP7. or tis purpose, a sample study was performed in a simulation environment [8]. igure 2 sows te comparison of te selected posture s power consumption and fied posture (θ redundant = 0) power consumption for a specified task. Te optimal posture selection reduces te power consumption remarkably. Te cost function of te problem corresponds to te minimization of te total driving torques (τ), wic can be represented in terms of applied forces and Jacobian matri J : ind θ redundant (θ 3 ) to minimize te parasitic forces f (θ 3 ) = τ 1 τ 2... τ 7. Power (W) θ 3 power min θ 3 = Time (s) igure 2. Te comparison of te selected posture and fied posture power consumptions. 4. inematic and singularity analysis Te position and orientation of te manipulator are represented by a set of equations in te forward kinematic analysis. Te eponential rotation matrices are used to derive te kinematic equations in tis study. It enables te representation of te equations in simple and compact form [9]. Te orientation transformation matri and te position of te aptic andle can be derived as follows: Ĉ (0,7) = eũ3θ1 eũ2θ2 eũ3θ3 eũ2θ4 eũ3θ5 eũ2θ6 eũ3θ7, (1) 495

4 BAŞER and ONUSEVEN/Turk J Elec Eng & Comp Sci r = d 3 eũ3θ1 eũ2θ2 ū 3 d 4 eũ3θ1 eũ2θ2 eũ3θ3 eũ2θ4 ū 3. (2) Inverse kinematic solutions are indispensable for forwarding te end effector to any desired position and determining te singular configurations. It is possible to derive te inverse kinematic equations using analytical and semianalytical metods for a 6DO manipulator [10]. Te inverse kinematic of te redundant manipulator as infinitely many solutions. In order to find te inverse kinematic solutions for tis type of manipulator, one of te joint variables can be defined and te oter variables can be solved in terms of te defined variable. Te fourt joint variable (θ 4 ) of te HaP7 can be solved analytically witout using te oter variables and it can be used to find oter variables. Te inverse kinematic solutions based on defined joint variable θ 3 and singular configurations of te HaP7 can be derived as follows: Inverse kinematic solution based on te defined joint variable θ 3 : θ 4 = σ cos 1 2 y 2 z 2 d 2 3 d 2 4 2d 3 d 4 σ = 1. (3) θ 1 = atan 2 [ 2t1, 1 t 2 1], (4) were, t 1, η 2, ξ 2 (s: sine, c: cosine): θ 2 = atan 2 [η 2, ξ 2 ], (5) t 1 = 2 y 2 (sθ 3 sθ 4 d 4 ) 2, sθ 3 sθ 4 d 4 y η 2 = zcθ 3sθ 3 d 4 (cθ 1 sθ 1 y) (d 3 d 4 cθ 4 ) 2 c 2 θ 1 y 2 s 2 θ 1 2ysθ 1 cθ 1 z 2, ξ 2 = (cθ 1 sθ 1 y) cθ 3 sθ 3 d 4 z(d 3 d 4 cθ 4 ) 2 c 2 θ 1 y 2 s 2 θ 1 2ysθ 1 cθ 1 z 2. Te inverse kinematic equations do not give any solutions in singular configurations. Tese are: ±π. 1. Sing. θ 2 = 0, ±π ; 2. Sing. θ 4 = 0, ±π ; 3. Sing. = y = 0, 4. Sing. θ 6 = 0, 5. orce feedback control of te HaP7 and VR interface Tere are 2 basic control algoritms in aptic devices: impedance and admittance [11]. In te impedance type of control, te user s and motion is sensed and a reference force is computed based on te motion and virtual model. Te computed reference is sent to actuator drivers and is called te open loop impedance control (OLIC). Tis type of control strategy can be improved using a force feedback loop by means of a force transducer, wic is called te closed loop impedance control (CLIC). It enables te virtual environment to be sensed more accurately. In te admittance control (AC) algoritm, te motion is controlled to reflect te desired force. A reference motion is computed based on te user s force and virtual model and sent to te actuator drivers. Te AC algoritm requires a force transducer. Te appropriate control algoritm can be selected based on te virtual environment and te device itself. Te block diagram of te control algoritm types are sown in igure 3 (: motion, : force, S: sensor, C: controller, Z d : virtual model impedance, Z : aptic device impedance, Z 1 d : virtual model admittance, Z 1 : aptic device admittance, HD: aptic device). 496

5 BAS ER and ONUSEVEN/Turk J Elec Eng & Comp Sci d Zd Z 1 d Zd C S Z 1 S Z 1 C HD (c) igure 3. OLIC, CLIC, and AC (c) algoritms. igure 4 sows te eperimental setup of te HaP7 in te development of te control strategies. Tere are 2 computers in te setup. One of tem is te ost PC, devoted to developing te algoritms in MATLAB, and te oter is te target PC, devoted to te control of te device. Te applications running on te target PC are modeled using MATLAB/Simulink and te PC Target R libraries on te ost PC, wic are sent to te target PC via a LAN connection. Te virtual environments are modeled using te VRML language and tey are simulated using te 3DAnimation Toolbo on te ost PC. Te embedded control model in te target PC performs te manipulation of te motion/torque signals of te sensors and te computation of te reference analog voltage to te drivers. An OLIC algoritm is used for te implementation of te HaP7 in tis study. It receives te position information from te encoders and estimates te velocity and acceleration, and it computes te reference torque based on te virtual model, consisting of masses, springs, and dampers. Te analog voltage corresponding to te reference torque is applied to te motor drivers. Tus, te virtual environment is sensed by te user. Te motion information and motor torque reference outputs of te HaP7 are updated at 1 khz in te applications. (c) igure 4. Eperimental setup, VR interface of te HaP7, and grapical user interface (c). Te VR interface of te HaP7 was developed in te MATLAB/Simulink 3DAnimation Toolbo (igure 3). An elastic spere is considered in te applications. It is modeled as a spring cluster coming up to te surface from te center. Te user senses te force feedback at a perpendicular direction of te surface wen te andle is pused into te spere. Te sensed force depends on te spring coefficient and deflection of te springs. A grapical user interface was developed for te HaP7, wic enables te user to adjust te stiffness of te model using a slider bar (igure 4). In tis implementation, te HaP7 is considered as an ideal device and its dynamic nature and electronic driver effects are ignored. Te MATLAB/Simulink models for te force feedback and visual feedback are composed of 2 models (igure 5). Te motion information of te andle to be used for te VR interface is manipulated wit te signal names from te force feedback model to te visual feedback model. Tus, te VR implementation of te HaP7 497

6 BAŞER and ONUSEVEN/Turk J Elec Eng & Comp Sci is run on 2 MATLAB/Simulink models. One of te motors of te device is locked and te device is considered as a 6DO manipulator in te eperiments. Encoder Encoder1 inematic block TET1 ORIENT Direction cosine matri Target scope Encoder inematic Virtual reality block Encoder3 TET2 TET3 X X T1 Motor1 Encoder1 TET1 TET2 ORIENT Rotation matri to VRML rotation PEN ORIENTATION TET4 TET5 Y Y T2 Motor2 Encoder3 TET3 TET4 X Z Encoder7 TET6 TET7 Z T3 Motor3 180 TET5 TET6 Y PEN TRANSLATION Spring constant TET3 T4 Jacobian Motor4 Motor Encoder7 igure 5. MATLAB/Simulink models of te force feedback and visual feedback. TET7 Z Conclusion In tis study, a redundant HaP7 design is presented and te superiority of te design is put forward. A sample VR interface was developed in te MATLAB/Simulink 3DAnimation Toolbo. Te design of te device was performed by considering te maimum workspace, maimum force and torque, maimum rigidity, minimum backlas, and minimum apparent mass. Te device as 20% etra workspace witout compromising te oter design parameters compared to similar 6DO designs wit te same effective link lengts. Te OLIC strategy was used in te implementations. As a future work, te CLIC strategies will be applied and te performance of te device will be improved by implementing te optimal posture selection metodology using te redundancy of te device. References [1] MerriamWebster s Nint New Collegiate Dictionary, Springfield, MA, USA, MerriamWebster, [2] D.T. Burns, Design of a Si Degrees of reedom Haptic Device, MSc tesis, Nortwestern University, Evanston, IL, USA, [3] G.C. Burdea, orce and Touc eedback for Virtual Reality, New York, Wiley, [4] Ö. Başer, Haptic Device Design, MSc tesis, Middle East Tecnical University, Ankara, [5] Ö. Başer, E.İ. onukseven, 7 DO aptic device design, Euroaptics 2006 Conference, pp , [6] J. Werkmeister, A. Slocum, Teoretical and eperimental determination of capstan drive stiffness, Precision Engineering, Vol. 31, pp , [7] S.T. McJunkin, Transparency Improvement for Haptic Interfaces, PD tesis, Rice University, Houston, TX, USA,

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