Haptic rendering of objects with rigid and deformable parts

Abstract

In many haptic applications, the user interacts with the virtual environment through a rigid tool. Tool-based interaction is suitable in many applications, but the constraint of using rigid tools is not applicable to some situations, such as the use of catheters in virtual surgery, or of a rubber part in an assembly simulation. Rigid-tool-based interaction is also unable to provide force feedback regarding interaction through the human hand, due to the soft nature of human flesh. In this paper, we address some of the computational challenges of haptic interaction through deformable tools, which forms the basis for direct-hand haptic interaction. We describe a haptic rendering algorithm that enables interactive contact between deformable objects, including self-collisions and friction. This algorithm relies on a deformable tool model that combines rigid and deformable components, and we present the efficient simulation of such a model under robust implicit integration.

Introduction

Haptic rendering is the computational technology that allows us to interact with virtual worlds through the sense of touch. It relies on an algorithm that simulates a virtual world in a physically based manner and computes interaction forces, and on a robotic device that transmits those interaction forces to the user. Haptics science is a multidisciplinary field that brings together psychophysics research for the understanding of tactile cues and human perception; mechanical engineering for the design of robotic devices; control theory for the analysis of the coupling between the real and virtual worlds; and computer science, in particular computer graphics, for the simulation of the virtual world and the design of the haptic rendering algorithm [29].

In this paper, we focus on the haptic rendering of objects that are composed of both rigid and deformable parts. Many of the objects in the real world, including our own flesh, fit this description. In particular, our haptic rendering algorithm serves as the main building block for model-based computation of direct-hand haptic interaction. The hand is the main tactile sensor used by humans to capture information from the world [25]. It allows us to manipulate the world and provides us with two-way interaction with our environment. Despite the importance of the human hand for haptic interaction, current haptic devices and haptic rendering techniques suffer important limitations that have not allowed hand-based virtual touch to reach its full potential. Haptic rendering is typically carried out either through a pen-like robotic device, or through vibrotactile devices. In addition to hardware limitations, most haptic rendering algorithms are limited to point-based interaction between the user and the objects in the environment. There are some notable exceptions, both devices (e.g., exoskeleton structures [23], [7], [33]) and object-object rendering algorithms, also called 6-Degree-of-Freedom (6-DoF) haptic rendering [31], [39], [6].

We follow a strategy for haptic rendering of tool-based contact where a virtual replica of the tool is simulated in a virtual world, and haptic interaction takes place through a viscoelastic coupling between the haptic device and the tool [11]. Following this strategy, direct-hand touch can be rendered by simulating a virtual hand as the tool (as shown in Fig. 1), and coupling the device to this simulated hand. In Section 3, we summarize the adaptation of a multirate 6-DoF haptic rendering algorithm to model multipoint contact with objects composed of rigid and deformable parts, such as a hand. This algorithm does not suffer from the limitations of traditional single-point contact models for capturing the interaction between soft fingers and the environment.

In Section 4, taking the hand as an example model, we describe how to connect rigid and deformable components and how to actuate them through standard haptic devices. We exploit the position and orientation tracked by a haptic device to guide the rigid components of the virtual hand, and we model the coupling between the rigid and deformable components of the hand using stiff connections and implicit integration. As a first step toward full-hand haptic rendering, we consider the hand to be a shape formed by one rigid component and elastic flesh, and we do not take into account the articulations of the fingers.

A computational algorithm, described in Section 5, allows us to simulate a virtual hand using existing implementations of rigid-body and deformable-body simulations as black boxes. The use of implicit integration couples the degrees of freedom of the rigid and deformable components of the virtual hand, but our algorithm allows us to work around these couplings and still use existing implementations as black boxes.

We show our haptic rendering algorithm applied to the interaction between a hand model and other complex deformable objects with friction (see Fig. 5), with several moving deformable objects (see Fig. 6), and with self-collisions between the fingers (see Fig. 3). In Section 6, we also analyze the impact of various parameters of the virtual scene on the computational cost of our haptic rendering algorithm.