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Research Papers

Energy-Consistent Force Feedback Laws for Virtual Environments

[+] Author and Article Information
Arash Mohtat

e-mail: amohtat@cim.mcgill.ca

József Kövecses

e-mail: jozsef.kovecses@mcgill.ca
Department of Mechanical Engineering and Centre for Intelligent Machines,
McGill University
Montreal, Québec, Canada

A system is called BIBO stable if it has bounded gain. Refer to [26] for more details.

In the absence of any physical dissipation such as viscous damping or friction, the closed loop will be only critically stable. The undamped physical mass is a simple example of such a worst-case scenario that will be used later.

In this paper we will only deal with such VEs, i.e., VEs whose continuous-time counterparts are passive.

The sign convention is consistent: Passivity violation is implied by a positive leak reflected into energy expressions through a negative sign.

The “impulsive” behavior (sudden spiky reactions) of the basic POPC is not a result of singularity. Even when the singularity is avoided in the aforementioned way, the basic POPC will still exhibit spiky reactions (see Fig. 2). This behavior originates from the very wait-then-react policy of the basic POPC, i.e., waiting for accumulation and then attempting to dissipated all the accumulated violation in a single step.

The POPC-REF, as a nonlinear operation, does not seem to lend itself to such a simple symbolic analysis. The approximate limit κ=0.96 is obtained via simulation and contains overestimation due to artificial dissipation of numerical solvers.

This refers to no net energy generation over the event, and is different from exact (interval-wise) passivity in its strict sense.

This convention has been satisfied in all previous derivations, e.g., the spring force is considered Kx (and not -Kx). Figure 5(b) clearly obeys this convention.

A pure force source can be considered a worst-case scenario for impedance devices [31].

The leaks are about 400 times smaller at this rate.

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Computing and Information Science in Engineering. Manuscript received February 6, 2013; final manuscript received February 25, 2013; published online May 14, 2013. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 13(3), 031003 (May 14, 2013) (13 pages) Paper No: JCISE-13-1018; doi: 10.1115/1.4023918 History: Received February 06, 2013; Revised February 25, 2013

When digitally realized, virtual environments (VEs) do not perfectly match the physical environments they are supposed to emulate. This paper deals with energy aspects of such a mismatch, i.e., artificial energy leaks. A methodology is developed that employs smooth correction (SC) and leak dissipation (LD) to achieve a stable interconnection of the VE with the haptic device. The SC-LD naturally blends with the original laws for rendering the VE and gives rise to modified force feedback laws. These laws can be regarded as energy-consistent discretizations of their continuous-time counterparts. For some fundamental examples including virtual springs and masses, these laws are analytically reduced to simple closed-form equations. The methodology is then generalized to the multivariable case. Several experiments are conducted including a 2-DOF coupled nonlinear VE example, and a scenario leading to a sequence of contacts with a virtual object. Besides the conceptual advantage, simulation and experimental results demonstrate some other advantages of the SC-LD over well-known time-domain passivity methods. These advantages include improved fidelity, simpler implementation, and less susceptibility to produce impulsive/chattering response.

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References

Hannaford, B., and Okamura, A., 2008, Handbook of Robotics, Springer, Berlin, pp. 719–739.
Ueberle, M., and Buss, M., 2004, “Control of Kinesthetic Haptic Interfaces,” IEEE/RSJ Int. Conf. on Intell. Robots and Syst., Workshop on Touch and Haptics.
Flugge, W., 1967, Viscoelasticity, Blaisdell, Waltham, MA.
Gillespie, R., and Cutkosky, M., 1996, “Stable User-Specific Haptic Rendering of the Virtual Wall,” Proc. ASME Int. Mech. Eng. Congress and Exhibition, 58, pp. 397–406.
Kövecses, J., Kovács, L., and Stépán, G., 2007, “Dynamics Modeling and Stability of Robotic Systems With Discrete-Time Force Control,” Arch. Appl. Mech., 77(5), pp. 293–299. [CrossRef]
Colgate, J., and Schenkel, G., 1994, “Passivity of a Class of Sampled-Data Systems: Application to Haptic Interfaces,” Am. Control Conf., 3, pp. 3236–3240. [CrossRef]
Abbott, J., and Okamura, A., 2005, “Effects of Position Quantization and Sampling Rate on Virtual-Wall Passivity,” IEEE Trans. Robot., 21(5), pp. 952–964. [CrossRef]
Diolaiti, N., Niemeyer, G., Barbagli, F., and Salisbury, J., 2006, “Stability of Haptic Rendering: Discretization, Quantization, Time Delay, and Coulomb Effects,” IEEE Trans. Robot., 22(2), pp. 256–268. [CrossRef]
An, J., and Kwon, D., 2006, “Stability and Performance of Haptic Interfaces With Active/Passive Actuators—Theory And Experiments,” Int. J. Robot. Res., 25(11), pp. 1121–1136. [CrossRef]
Gil, J., Sánchez, E., Hulin, T.Preusche, C., and Hirzinger, G., 2009, “Stability Boundary for Haptic Rendering: Influence of Damping and Delay,” ASME J. Comput. Inform. Sci. Eng., 9, p. 011005.
Hannaford, B., and Ryu, J., 2002, “Time-Domain Passivity Control of Haptic Interfaces,” IEEE Trans. Robot. Autom., 18(1), pp. 1–10. [CrossRef]
Hogan, N., 1989, “Controlling Impedance at the Man/Machine Interface,” 1989 IEEE Int. Conf. Robot. Autom., pp. 1626–1631.
Colgate, J., Stanley, M., and Brown, J., 1995, “Issues in the Haptic Display of Tool Use,” 1995 IEEE/RSJ Int. Conf. Intell. Robots Syst., Vol. 3, IEEE, pp. 140–145.
Zilles, C., and Salisbury, J., 1995, “A Constraint-Based God-Object Method for Haptic Display,” 1995 IEEE/RSJ Int. Conf. Intell. Robots Syst., Vol. 3, IEEE, pp. 146–151.
Adams, R., and Hannaford, B., 1999, “Stable Haptic Interaction With Virtual Environments,” IEEE Trans. Robot. Autom., 15(3), pp. 465–474. [CrossRef]
Miller, B., Colgate, J., and Freeman, R., 1999, “Passive Implementation for a Class of Static Nonlinear Environments in Haptic Display,” 1999 IEEE Int. Conf. Robot. Autom., Vol. 4, IEEE, pp. 2937–2942.
Iqbal, A., and Roth, H., 2006, “Predictive Time Domain Passivity Control for Delayed Teleoperation Using Energy Derivatives,” 9th Int. Conf. Control, Autom., Robot. Vision, IEEE, pp. 1–6.
Ryu, J., Preusche, C., Hannaford, B., and Hirzinger, G., 2005, “Time Domain Passivity Control With Reference Energy Following,” IEEE Trans. Control Syst. Tech., 13(5), pp. 737–742. [CrossRef]
Hertkorn, K., Hulin, T., Kremer, P., Preusche, C., and Hirzinger, G., 2010, “Time Domain Passivity Control for Multidegree of Freedom Haptic Devices With Time Delay,” 2010 IEEE Int. Conf. Robot. Autom., IEEE, pp. 1313–1319.
Ott, C., Artigas, J., and Preusche, C., 2011, “Subspace-Oriented Energy Distribution for the Time Domain Passivity Approach,” 2011 IEEE/RSJ Int. Conf. Intell. Robots Syst.
Stramigioli, S., Secchi, C., van der Schaft, A., and Fantuzzi, C., 2002, “A Novel Theory for Sampled Data System Passivity,” 2002 IEEE/RSJ Int. Conf. Intell. Robots Syst., Vol. 2, IEEE, pp. 1936–1941.
Borghesan, G., Macchelli, A., and Melchiorri, C., 2010, “Interconnection and Simulation Issues in Haptics,” Vol. 3, IEEE Trans. Haptics, pp. 266–279. [CrossRef]
Lee, D., and Huang, K., 2010, “Passive-Set-Position-Modulation Framework for Interactive Robotic Systems,” IEEE Trans. Robot., 26(2), pp. 354–369. [CrossRef]
Lee, D., Kim, M., and Qiu, T., 2012, “Passive Haptic Rendering and Control of Lagrangian Virtual Proxy,” 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, pp. 64–69.
Slotine, J., and Li, W., 1991, Applied Nonlinear Control, Prentice Hall Englewood Cliffs, NJ, Vol. 66.
Aström, K., and Wittenmark, B., 1994, Adaptive Control, 2nd ed., Addison-Wesley, Reading, MA.
Ryu, J., Kim, Y., and Hannaford, B., 2004, “Sampled- and Continuous-Time Passivity and Stability of Virtual Environments,” IEEE Trans. Robot., 20(4), pp. 772–776. [CrossRef]
Ellis, R., Sarkar, N., and Jenkins, M., 1997, “Numerical Methods for the Force Reflection of Contact,” ASME Trans. Dyn. Syst. Meas. Control, 119, pp. 768–774. [CrossRef]
Levine, W., 1996, The Control Handbook, Control System Fundamentals, CRC, Boca Raton, FL.
Preusche, C., Hirzinger, G., Ryu, J., and Hannaford, B., 2003, “Time Domain Passivity Control for 6 Degrees of Freedom Haptic Displays,” 2003 IEEE/RSJ Int. Conf. Intell. Robots Syst., Vol. 3, pp. 2944–2949.
Constantinescu, D., Salcudean, S., and Croft, E., 2005, “Haptic Rendering of Rigid Contacts Using Impulsive and Penalty Forces,” IEEE Trans. Robot., 21(3), pp. 309–323. [CrossRef]
Miller, B., Colgate, J., and Freeman, R., 2004, “On the Role of Dissipation in Haptic Systems,” IEEE Trans. Robot., 20(4), pp. 768–771. [CrossRef]
Kim, J., and Ryu, J., 2010, “Robustly Stable Haptic Interaction Control Using an Energy-Bounding Algorithm,” Int. J. Robot. Res., 29(6), pp. 666–679. [CrossRef]

Figures

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Fig. 1

The closed-loop feedback interconnection of the haptic device HHD and the target environment HT

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Fig. 2

The VS corrected by different POPC methods

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Fig. 3

The VS corrected by the basic SC method

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Fig. 4

The VS corrected by different SC methods

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Fig. 5

The VS-VM example: (a) schematic and (b) block-diagram interconnection

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Fig. 6

Simulation of physical mass colliding to a VO

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Fig. 7

The SC implemented in EP coordinates

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Fig. 8

(a) The 2-DOF haptic device. (b) Notation.

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Fig. 9

Experiment 1a results: K=250N/m at 50Hz

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Fig. 10

Experiment 1b results: K = 300 N/m at 500 Hz

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Fig. 11

Experiment 1b results: K = 3000 N/m at 500 Hz

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Fig. 12

The contact experiment

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Fig. 13

Experimental results: K = 100 N/m at 50 Hz

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