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Research Papers

# High-Fidelity Rendering of Contact With Virtual Objects

[+] Author and Article Information
Arash Mohtat

Department of Mechanical Engineering and
Centre for Intelligent Machines,
McGill University,
e-mail: amohtat@cim.mcgill.ca

József Kövecses

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

Usually selected as the effective mass at the end point of the device.

For simplicity, now, we shall assume fV to be independent of the VO states. In Sec. 4.2, it will be briefly discussed what happens otherwise.

Note that in this figure, the VS is just a graphical visualization of the concept; hence, we do not need to associate a length to the spring.

In haptics, model-based prediction of velocity is not very useful, mainly due to the unknown influence of the user. Other possibilities are the constant mean velocity approximation and extrapolation. We will use the simplest approximation, and deal with the remaining leaks afterwards.

Note that the energy balance depends only on the two end points of the interval, and not the intersample transition. The unit step $h(.)$ in the $S˜i+1$ formulation automatically takes into account the predicted contact mode at the end point.

Under many operational conditions, including this experiment, the human has a favorable effect on stability. Hence, replacing the operator by a force source can be considered a worst-case evaluation.

The term (un-)coupled refers to whether (or not) a human arm model is connected to the device.

Due to the log-scaling, this curve is not seen as a straight line in the figures.

$v$ should form a consistent power pair with $fVE$. Since the latter is usually expressed in the task-space, so is the former (i.e., end-effector velocity). Alternatively, they can be both formulated in the joint space.

Unless a seventh motor is attached at the bottom of the handle, to provide for spin actuation.

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 4, 2013; final manuscript received December 19, 2014; published online March 26, 2015. Assoc. Editor: Evangelos Papadopoulos.

J. Dyn. Sys., Meas., Control 137(7), 071009 (Jul 01, 2015) (12 pages) Paper No: DS-13-1427; doi: 10.1115/1.4029465 History: Received November 04, 2013; Revised December 19, 2014; Online March 26, 2015

## Abstract

When interacting with a virtual object (VO) through a haptic device, it is crucial to feedback a contact force to the human operator (HO) that displays the VO physical properties with high fidelity. The core challenge, here, is to expand the renderable range of these properties, including larger stiffness and smaller inertia, at the available sampling rate. To address this challenge, a framework entitled high-fidelity contact rendering (HFCR) has been developed in this paper. The framework consists of three main strategies: an energy-based rendering of the contact force, smooth transition (ST) between contact modes, and remaining leak dissipation (LD). The essence of these strategies is to make the VO emulate its continuous-time counterpart. This is achieved via physically meaningful modifications in the constitutive relations to suppress artificial energy leaks. The strategies are first developed for the one-dimensional (1D) canonical VO; then, generalization to the multivariable case is discussed. Renderability has been analyzed exploring different stability criteria within a unified approach. This leads to stability charts and identification of renderable range of properties in the presence and absence of the HO. The framework has been validated through simulation and various experiments. Results verify its promising aspects for various scenarios including sustained contact and sudden collision events with or without the HO.

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## Figures

Fig. 1

Direct versus indirect rendering: (a) The device directly receives the penalty-based force when it contacts the VO. (b) The contact force developed between the VO and the virtual tool mass is indirectly fed to the device via the VC.

Fig. 2

The VS–VM system for modeling the VO in contact mode: schematic (a) and block-diagram (b)

Fig. 3

The VO simulation at κ=K=0.1: step-by-step development of the HFCR, i.e., modified law + ST + LD, framework: (a) Leak accumulation over time (the ideal case has zero leaks) and (b) rendered force

Fig. 4

Comparison of force rendering fidelity achieved by the SEH filter, the POPC–REF, a properly tuned VD, and the HFCR method developed in this paper

Fig. 5

(a) The 2DOF haptic device and (b) the experiment

Fig. 10

Stability chart in the (κ,K) log–log plane at 1 kHz

Fig. 9

Grouping the haptic system components as the feedback interconnection of: (a) two continuous-time systems, i.e., (Pc;Qc), where Pc is the plant (device and HO) and Qc is the continuous-time realization of the VO; (b) two discrete-time systems, i.e., (P;Q), where P is the discretized plant and Q is the discrete-time impedance function of the VO

Fig. 8

Experimental results for the sliding virtual box

Fig. 7

The falling virtual ball at (κ,K) = (0.64,1.6)

Fig. 6

The falling virtual ball at (κ,K) = (0.16,0.4)

Fig. 11

Stability chart in the (κ,K) log–log plane at 100 Hz

Fig. 12

Experimental results at κ = 0.2 and K = 0.5 (a) and K = 4 (b)

Fig. 13

The W5D device and the 3DOF virtual pendulum

Fig. 14

Experimental results with the W5D device: (a) rendered force for the 3DOF pendulum and (b) correction force

## Errata

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