Bilateral teleoperation of a pneumatic actuator: experiment and stability analysis
DOI:
https://doi.org/10.1080/14399776.2015.1064663Keywords:
pneumatic actuator, bilateral teleoperation, sliding mode control, stability analysis, Lyapunov exponentsAbstract
This paper presents design, implementation and stability analysis of a bilateral teleoperated pneumatic actuation system whereby a low-cost pneumatic actuator is navigated by an operator using a commercially-available haptic device. The actuator is subject to an external force, the value of which is scaled and rendered on the haptic device to provide the operator with a feeling of the interaction at the remote site. Sliding mode control scheme is implemented for positioning the pneumatic actuator. The performance of the system is experimentally evaluated through several experiments including interaction with springs having different stiffnesses and an arbitrary resistive/assistive force applied by a human at the actuator side. Stability of the entire system is theoretically proven using the concept of Lyapunov exponents that quantitatively measures convergence/divergence of initially infinitely close solution trajectories.
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References
Al-Dakkan, K., Barth, E., and Goldfarb, M., 2006. Dynamic
constraint-based energy-saving control of pneumatic servo
systems. Journal of dynamic systems, measurement, and
control, 128 (3), 655–662.
Aliaga, I., Rubio, A., and Sanchez, E., 2004. Experimental
quantitative comparison of different control architectures
for master-slave teleoperation. IEEE transactions on control
systems technology, 12 (1), 2–11.
Bone, G. and Ning, S., 2007. Experimental comparison of
position tracking control algorithms for pneumatic cylinder
actuators. IEEE/ASME transactions on mechatronics, 12
(5), 557–561.
Canudas de Wit, C., Olsson, H., Astrom, K., and Lischinsky,
P., 1995. A new model for control of systems with friction.
IEEE transactions on automatic control, 40 (3), 419–425.
Durbha, V. and Li, P.Y., 2009. Passive bilateral teleoperation
and human power amplification with pneumatic actuators.
In: Proceedings of the ASME 2009 dynamic systems and
control conference, 12–14 October, Hollywood, CA,
–870.
Durbha, V. and Li, P.Y., 2010. Passive tele-operation of pneumatic
powered robotic rescue crawler. In: Proceeding of
th FPNI-PhD symposium, 15–19 June, West Lafayette,
IN, 451–466.
Filippov, A., 1960. Differential equations with discontinuous
right-hand sides. Math Sbornnik, 51, 99–128 [English
Translation: American Mathematical Society Translations,
, 199–231, 1964].
Filippov, A., 1988. Differential equations with discontinuous
right-hand sides. Dordrecht, ND: Kluwer Academic
Publishers.
Gulati, N. and Barth, E., 2009. A globally stable, load-independent
pressure observer for the servo control of pneumatic
actuators. IEEE/ASME transactions on mechatronics, 14 (3),
–306.
Hannaford, B., 1989. A design framework for teleoperators
with kinesthetic feedback. IEEE transactions on robotics
and automation, 5 (4), 426–434.
Hodgson, S., Le, M., Tavakoli, M., and Pham, M., 2012.
Improved tracking and switching performance of an electro-
pneumatic positioning system. Mechatronics, 22, 1–12.
Hogan, N., 1989. Controlling impedance at the man/machine
interface. In: Proceeding of IEEE international conference
on robotics and automation, 14–19 May, Scottsdale, AZ,
–1631.
Hogan, N. and Buerger, S.P., 2004. Impedance and Interaction
Control. Chapter 19. In: Robotics and automation handbook.
New York, NY: CRC Press, 1–24.
Jouppila, V., et al., 2014. Sliding mode control of a pneumatic
muscle actuator system with a PWM strategy. International
journal of fluid power, 15 (1), 19–31.
Karpenko, M. and Sepehri, N., 2006. Development and experimental
evaluation of a fixed-gain nonlinear control for a
low-cost pneumatic actuator. IEE proceedings of control
theory and applications, 153 (6), 629–640.
Khalil, H., 1995. Nonlinear systems. Upper Saddle River, NJ:
Prentice Hall.
Kontz, M. and Book, W., 2007. Flow control for coordinated
motion and haptic feedback. International journal of fluid
power, 8, 13–23.
Kunze, M., 2000. Non-smooth dynamical systems. Berlin:
Springer-Verlag.
Leleve, A., Pham, M.T., Tavakoli, M., and Moreau, R., 2012.
Towards delayed teleoperation with pneumatic master and
slave for MRI. In: ASME 11th biennial conference on engineering
systems design and analysis, July 2–4, Nantes,
–846.
Le, M., et al., 2013. Bilateral control of nonlinear pneumatic
teleoperation system with solenoid valves. IEEE transaction
on control systems technology, 21 (4), 1463–1470.
Li, H., Tadano, K., and Kawashima, K., 2012. Achieving force
perception in master-slave manipulators using pneumatic
artificial muscles. In: SICE annual conference, 20–23
August, Akita, 342–1345.
Morales, R., Badesa, F.J., Garcia-Aracil, N., Sabater, J.M., and
Perez-Vidal, C., 2011. Pneumatic robotic systems for upper
limb rehabilitation. Journal of medical & biological
engineering & computing, 49 (10), 1145–1156.
Müller, P., 1995. Calculation of Lyapunov exponents for
dynamic systems with discontinuities. Chaos, solitons &
fractals, 5 (9), 1671–1681.
Oseledec, V., 1968. A multiplicative ergodic theorem:
Lyapunov characteristic numbers for dynamical system.
Transaction of Moscow math society, 19, 197–231.
Sadri, S. and Wu, C., 2013. Stability analysis of a nonlinear
vehicle model in plane motion using the concept of
Lyapunov exponents. International journal of vehicle
mechanics and mobility, 51 (6), 906–924.
Sanville, F.E., 1971. A new method of specifying the flow
capacity of pneumatic fluid power valves. In: BHRA 2nd
international fluid power symposium, Guildford, 37–47.
Sekhavat, P., Sepehri, N., and Wu, C.Q., 2005. Overall stability
analysis of hydraulic actuator’s switching contact control
using the concept of Lyapunov exponents. In: Proceedings
of the IEEE international conference on robotics and
automation, 18–22 April, Barcelona, 550–556.
Shen, X., 2010. Nonlinear model-based control of pneumatic
artificial muscle servo systems. Control engineering
practice, 18, 311–317.
Sun, Y. and Wu, C., 2013. Stability analysis via the concept of
Lyapunov exponents: a case study in optimal controlled
biped standing. International journal of control, 85 (12),
–1966.
Wolf, A., Swift, J., Swinney, H., and Vastano, J., 1985.
Determining Lyapunov exponents from a time series.
Journal of physica, 16 (4), 285–317.
Wu, J., Goldfarb, M., and Barth, E., 2004. On the observability
of pressure in a pneumatic servo actuator. Journal of
dynamic systems, measurement, and control, 126, 921–924.
Yang, C., Wu, C., and Zhang, P., 2012. Estimation of
Lyapunov exponents from a time series for n-dimensional
state space using nonlinear mapping. Nonlinear dynamics,
, 1493–1507.
Zarei-nia, K. and Sepehri, N., 2012. Lyapunov stable
displacement-mode haptic manipulation of hydraulic
actuators: theory and experiment. International journal of
control, 85 (9), 1313–1326.
