Cable Tension Control and Analysis of Reel Transparency for 6-DOF Haptic Foot Platform on a Cable-Driven Locomotion Interface

A Cable-Driven Locomotion Interface provides a low inertia haptic interface and is used as a way of enabling the user to walk and interact with virtual surfaces. These surfaces generate Cartesian wrenches which must be optimized for each motorized reel in order to reproduce a haptic sensation in both feet. However, the use of wrench control requires a measure of the cable tensions applied to the moving platform. The latter measure may be inaccurate if it is based on sensors located near the reel. Moreover, friction hysteresis from the reel moving parts needs to be compensated for with an evaluation of low angular velocity of the motor shaft. Also, the pose of the platform is not known precisely due to cable sagging and mechanical deformation. This paper presents a non-ideal motorized reel design with its corresponding control strategy that aims at overcoming the aforementioned issues. A transfert function of the reel based on frequency responses in function of cable tension and cable length is presented with an optimal adaptative PIDF controller. Finally, an hybrid position/tension control is discussed with an analysis of the stability for achieving a complete functionnality of the haptic platform.

Authors:

• Martin J.-D. Otis
• Thien-Ly Nguyen-Dang
• Thierry Laliberte
• Denis Ouellet
• Denis Laurendeau
• Clement Gosselin

Keywords:

• haptic
• reel
• transparency
• cable
• tension
• control

References:

[1] S. Perreault and C. Gosselin, "Cable-driven parallel mechanisms: application
to a locomotion interface," Journal of Mechanical Design,
Transactions of the ASME, vol. 130, no. 10, pp. 102 301-1-8, 10 2008.
[2] M. J.-D. Otis, M. Mokhtari, C. Du Tremblay, D. Laurendeau, F.-M.
De Rainville, and C. M. Gosselin, "Hybrid control with multi-contact
interactions for 6dof haptic foot platform on a cable-driven locomotion
interface," in Symposium on Haptics Interfaces for Virtual Environment
and Teleoperator Systems 2008 - Proceedings, Haptics, Piscataway, NJ
08855-1331, United States, 2008, pp. 161 - 168.
[3] J. E. Colgate and J. M. Brown, "Factors affecting the z-width of a
haptic display," in Proceedings of the IEEE International Conference
on Robotics and Automation, vol. 4, San Diego, CA, USA, 05 1994, pp.
3205 - 3210.
[4] R. Adams, D. Klowden, and B. Hannaford, "Stable haptic interaction
using the excalibur force display," in Proceedings of the IEEE International
Conference on Robotics and Automation, vol. 1, San Francisco,
CA, USA, 2000, pp. 770 - 5.
[5] I. Ebert-Uphoff and P. Voglewede, "On the connections between cabledriven
robots, parallel manipulators and grasping," in Proceeding of the
IEEE International Conference on Robotics and Automation, vol. 5, New
Orleans, LA, USA, 2004, pp. 4521 - 6.
[6] C. Bonivento, A. Eusebi, C. Melchiorri, M. Montanari, and G. Vassura,
"Wireman: a portable wire manipulator for touch-rendering of bas-relief
virtual surfaces," in Proceeding of the 8th International Conference on
Advanced Robotics, Monterey, CA, USA, 1997, pp. 13 - 18.
[7] K. Kozak, Q. Zhou, and J. Wang, "Static analysis of cable-driven
manipulators with non-negligible cable mass," IEEE Transactions on
Robotics, vol. 22, no. 3, pp. 425 - 33, 06 2006.
[8] E. Ottaviano, "A system for tension monitoring in cable-based parallel
architectures," in Proceedings of the 12th IFToMM World Congress,
Besanc┬©on, France, 06 2007.
[9] F. Ferlay and F. Gosselin, "A new cable-actuated haptic interface design,"
in Lecture Notes in Computer Science (including subseries Lecture Notes
in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5024
NCS, Heidelberg, D-69121, Germany, 2008, pp. 474 - 483.
[10] X. Diao and O. Ma, "Vibration analysis of cable-driven parallel manipulators
for hardware-in-the-loop contact-dynamics," in Proceedings of
the ASME International Design Engineering Technical Conferences &
Computer and Information in Engineering Conference, Las Vegas, NV,
September 2007.
[11] C. F. Baicu, C. D. Rahn, and B. D. Nibali, "Active boundary control of
elastic cables: Theory and experiments," Journal of Sound and Vibration,
vol. 198, no. 1, pp. 17 - 26, 1996.
[12] T. Kabayashi and Y. Takahashi, "Vibration control for two dimensional
wire driven positioning robot," in Proceedings of the 37th SICE Annual
Conference, Tokyo, Japan, 1998, pp. 869 - 74.
[13] M. Hiller, S. Fang, S. Mielczarek, R. Verhoeven, and D. Franitza,
"Design, analysis and realization of tendon-based parallel manipulators,"
Mechanism and Machine Theory, vol. 40, no. 4, pp. 429 - 445, 2005.
[14] J. Yoon and J. Ryu, "A novel locomotion interface with two 6-dof
parallel manipulators that allows human walking on various virtual
terrains," International Journal of Robotics Research, vol. 25, no. 7,
pp. 689 - 708, 07 2006.
[15] V. Duchaine and C. M. Gosselin, "Investigation of human-robot interaction
stability using lyapunov theory," in Proceedings - IEEE International
Conference on Robotics and Automation, Piscataway, NJ 08855-
1331, United States, 2008, pp. 2189 - 2194.
[16] B. Hannaford and J.-H. Ryu, "Time-domain passivity control of haptic
interfaces," IEEE Transactions on Robotics and Automation, vol. 18,
no. 1, pp. 1 - 10, 2002.
[17] S. Fang, D. Franitza, M. Torlo, F. Bekes, and M. Hiller, "Motion
control of a tendon-based parallel manipulator using optimal tension
distribution," IEEE/ASME Transactions on Mechatronics, vol. 9, no. 3,
pp. 561 - 8, 9 2004.
[18] D. Theodorakatos, E. Stump, and V. Kumar, "Kinematics and pose
estimation for cable actuated parallel manipulators," in Proceedings of
the ASME International Design Engineering Technical Conferences and
Computers and Information in Engineering Conference, vol. 8 PART B,
Las Vegas, NV, United States, 2008, pp. 1053 - 1062.
[19] M. J.-D. Otis, S. Perreault, T.-L. Nguyen-Dang, P. Lambert, M. Gouttefarde,
D. Laurendeau, and C. M. Gosselin, "Determination and management
of cable interferences between two 6-dof foot platforms in a
cable-driven locomotion interface," IEEE Transaction on Systems, Man
and Cybernetics, Part A, in press.
[20] F. Janabi-Sharifi, V. Hayward, and C.-S. Chen, "Discrete-time adaptive
windowing for velocity estimation," IEEE Transactions on Control
Systems Technology, vol. 8, no. 6, pp. 1003 - 1009, 11 2000.
[21] J. Canny, "A computational approach to edge detection," IEEE Transactions
on Pattern Analysis and Machine Intelligence, vol. PAMI-8, no. 6,
pp. 679 - 98, 11 1986.
[22] C. C. de Wit, H. Olsson, K. Astrom, and P. Lischinsky, "New model
for control of systems with friction," IEEE Transactions on Automatic
Control, vol. 40, no. 3, pp. 419 - 425, 1995.
[23] R. Kelly and J. Llamas, "Determination of viscous and coulomb friction
by using velocity responses to torque ramp inputs," IEEE International
Conference on Robotics and Automation, vol. 3, pp. 1740-1745, 1999.
[24] F.-J. Elmer, "Nonlinear dynamics of dry friction," Journal of Physics A:
Mathematical and General, vol. 30, no. 17, pp. 6057-6063, 1997.
[25] R. G. Lanzara, "Weber-s law modeled by the mathematical description
of a beam balance," Mathematical Biosciences, vol. 122, no. 1, pp. 89
- 94, 1994.
[26] V. Duchaine and C. M. Gosselin, "General model of human-robot
cooperation using a novel velocity based variable impedance control,"
in Second Joint EuroHaptics Conference and Symposium on Haptic
Interfaces for Virtual Environment and Teleoperator Systems, World
Haptics 2007, Piscataway, NJ 08855-1331, United States, 2007, pp. 445
- 451.
[27] W.-X. Ren, G. Chen, and W.-H. Hu, "Empirical formulas to estimate
cable tension by cable fundamental frequency," Structural Engineering
and Mechanics, vol. 20, no. 3, pp. 363 - 380, 2005.
[28] J.-C. Shen and H.-K. Chiang, "Pid tuning rules for second order
systems," in The 5th Asian Control Conference, vol. 1, Melbourne,
Australia, 7 2004, pp. 472-477.
[29] N. J. Killingsworth and M. Krstic, "Pid tuning using extremum seeking:
Online, model free-performance optimization," IEEE Control Systems
Magazine, vol. 26, no. 1, pp. 70 - 79, 2006.
[30] M. J.-D. Otis, T.-L. Nguyen-Dang, D. Laurendeau, and C. Gosselin,
"Extremum seeking tuning for reel tension control in haptic application,"
in Proceedings of the 2nd Mediterranean Conference on Intelligent
Systems and Automation, Zarzis, Tunesie, 03 2009.
[31] S. Shimano, M. Shiono, and K. Ohnishi, "Estimation of acceleration by
an ac tachogenerator and its applications to servo control," Electrical
Engineering in Japan, vol. 110, no. 6, pp. 90 - 7, 1990