M. Ferre (Ed.): EuroHaptics 2008, LNCS 5024, pp. 675 – 680, 2008. © Springer-Verlag Berlin Heidelberg 2008

Surface Contact Interaction with Dynamically Deformable Object Using Impulse-Based Approach

Kazuyoshi Tagawa1, Koichi Hirota2, and Michitaka Hirose1

1 Intelligent Modeling Laboratory, The University of Tokyo, Japan {tagawa,hirose}@cyber.t.u-tokyo.ac.jp

http://www.tagawa.info 2 Graduate School of Frontier Sciences, The University of Tokyo, Japan

k-hirota@k.u-tokyo.ac.jp

Abstract. In our previous study, a method that allows dynamic interaction with an elastic object, which is called impulse response deformation model, has been proposed. An advantage of the method is that the order of complexity is lower than other approaches that solve equations of deformation models in real time; hence the method enables haptic interaction with more complex object. In this paper, an extension of the model that enables efficient computation of elastic deformation in interaction with surfaces, such as floor and wall, is discussed; unlike point-based interaction in our previous studies, pre-recorded response to impulse force that is applied by surface rather than point is used for the computation.

Keywords: impulse response, deformation model, surface contact, elastic object.

1 Introduction

Recent advancement of computer network technologies has made information equip-ment closer to our daily lives. For intuitive and informal interaction with this equip-ment, multimodal interface that integrates a variety of sensations has been investigated. Haptic sensation is expected to be a useful information channel, and researches on device, sensing method, rendering algorithm, and recording and transmitting technolo-gies has been intensively conducted.

Representation of deformable objects is a fundamental topic in haptic rendering re-search. A focal issue is computational complexity of continuum dynamics model, and various approaches to reduce the complexity have been proposed.

In our previous study, a method that allows dynamic interaction with an elastic ob-ject, which is called impulse response deformation model, has been proposed [4]. An advantage of the method is that the order of complexity is lower than other ap-proaches that solve equations of deformation models in real time; hence the method enables haptic interaction with more complex object.

The method was initially applied to objects that are fixed to a floor; pressing and tracing on the surface for deformation were realized. In a subsequent study, the method was extended so that it enables interaction with non-grounded objects [5]; by integrating dynamics model, manipulation of elastic object was made possible.

676 K. Tagawa, K. Hirota, and M. Hirose

In this paper, another extension of the model that enables efficient computation of elastic deformation in interaction with surfaces such as floor and wall is discussed; unlike point-based interaction in our previous studies, pre-recorded response to im-pulse force that is applied by surface rather than point is used for the computation.

In the next section, related previous researches are surveyed. Our approach is stated in section 3, and its implementation and experimental evaluation are detailed in section 4, and attainment of this study is summarized in section 5.

2 Related Work

There are several approaches to representing deformable objects for haptic interac-tion. One approach is model-based simulation of deformation. A model that has been preferably used in virtual reality is spring-mass network [7] where a solution under given boundary condition is sought by iterative computation. Although this model is frequently computed at an identical update rate with haptic control, this computation method does not necessarily cause precise results on transient behavior of the object. Another model that is typically used for the simulation is FEM model [10]. In FEM computation, the solution of deformation is usually sought by solving simultaneous equations defined by the model. A critical problem of the computation for haptic application is complexity of computation, and several ideas to reduce computation time have been proposed. For example, Hirota et al accelerated the computation under the assumption that change of boundary condition is non-exhaustive [3]. However, this assumption does not hold in case of deformation that is caused by surface contact.

Another approach is reproduction of deformation based on recorded or precomputed data [11,8,9,6]. At present, this approach is advantageous to a model-based approach in reality of dynamic deformation. One sophisticated method is using precomputed trajec-tory in state space [2]; a drawback of the method is that the area of precomputation in state space rapidly expands as degrees of freedom of interaction increases.

An idea that enables dealing with large degrees of freedom is assuming linearity in force and deformation relationship. In our previous study, a model that represents the relationship by impulse response assuming linear time-invariant system, which is called impulse response deformation model, has been investigated[4]; a temporal sequence of deformation in response to impulse force has been precomputed in ad-vance, and resulting deformation according to interaction is computed by convolving interaction force with the impulse response data. Previous study focused on applica-tion to point-based interaction, and interaction with surface contact has been a subject for a further study.

3 Our Approach

3.1 Impulse Response Deformation Model

As stated in the previous section, impulse response deformation model (IRDM) is a model of dynamic deformation; the model consists of a set of deformation sequences according to the application of impulse force on each degree of freedom of the model. In case of interaction with a node, or a point on the model, usually the node has three degrees of freedom and responses to impulse force on each of them are recorded.

Surface Contact Interaction with Dynamically Deformable Object 677

Since complexity of computing deformation using IRDM is proportional to the number of nodes, or precisely the number of degrees of freedom, involved in the deforming operation, the model is substantively not applicable for interaction by sur-face contact that involves a large number of nodes.

3.2 Virtual Degree of Freedom

Although the model in our previous study was composed of response to impulse force on nodes, similar impulse response is obtained in other ways of interaction. Suppose a case when a surface collides with an elastic object. This interaction causes force and resulting deformation on the object, and the relationship is thought to be approxi-mately represented using impulse response. The degrees of freedom of translating or rotating the surface does not directly correspond to degrees of freedom of the deform-able object, however, it substantially serves as a degree of freedom in IRDM. In our study, degree of freedom of this type is called virtual degree of freedom.

In this paper, as an example that demonstrates an advantage of the virtual degree of freedom, interaction of an elastic model with frictionless infinite plane is stated. As shown in figure 1, the plane can approach to the object from various orientations, and it collides at a distance depending on the orientation. Since the plane is frictionless, it causes interaction force that is normal to the surface, hence the plane is considered to have only one degree of freedom. The orientations of the plane are discretely defined.

Contact Plains

ObjectShape

Contact Plains

ObjectShape

Fig. 1. Virtual degree of freedom

4 Experiment

4.1 Precomputation

An FEM model as shown in figure 2 was employed as a base model from which IRDM is constructed. The model consists of 2421 tetrahedral elements, 690 nodes (534 surface nodes), and 1796 surface patches; height of the model is approximately 20 cm, Young's modulus 23 N/m109.1 × , poisson ratio 0.40, and density 1100 3kg/m .

Orientations of plane normal for virtual degrees of freedom were defined using ori-entation of vertices of a geodesic dome; by subdividing regular icosahedron for two

678 K. Tagawa, K. Hirota, and M. Hirose

times, a polyhedron that has 162 vertices is obtained (see figure 3), and 162 degrees of freedom were defined using all vertices. Also, a position of plane that start to collide (or, distance of collision) for each degree of freedom was computed (see figure 3).

Fig. 2. Experimental model Fig. 3. Virtual degree of freedom of the model

For each virtual degree of freedom, deformation (i.e., displacements on surface nodes) caused by an impulsive force was computed; the impulsive force was applied by hitting the model with a rigid wall. This computation is performed using commer-cial software for finite element analysis (RADIOSS, Altair Engineering), running on a PC cluster that consists of 8 PCs (CPU: Xeon Core 2 Duo 2.6 GHz, memory: 2 GB). This software is capable of simulating deformation considering geometric nonlinearity. Computation time varies widely depending on degrees of freedom; the software auto-matically changes time step of simulation and it affects computation time. Figure 4 shows an example of impulse response in cases when plane collided with the object from the top of the cat shape.

Components of deformation and motion in the resulting behavior of the model were separated by matching the original shape with the deformed shape; position and orientation of the original shape that minimizes the square sum of distances of corre-sponding nodes were regarded as displacement that is caused by the component of motion and residual displacements from the original shape were regarded as the com-ponent of deformation [5]. Figure 4 (a) shows an example of the component of de-formation of impulse response on surface nodes. Affection of force on a virtual degree of freedom causes displacement (or, change in distance of plane) not only on surface nodes but also on other virtual degrees of freedom. The displacement was computed as follows: Firstly, when just after finished applying the impulsive force, nodes that are in the range of 1± mm from the plane were recorded. Next, average displacements of these nodes are computed, which was regarded as displacement on the virtual degree of freedom. Figure 4 (b) shows example of component of deforma-tion of impulse response on the virtual degree of freedom.

t=0 t=10 T=20 t=30 t=40 t=50ms

Fig. 4. Example of component of deformation of impulse response

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4.2 Experimental System

Experimental system consists of a PC (CPU:Quad Core Intel Xeon Processor 3.0GHz, memory:2GB, OS:Linux). Computation of force and deformation are performed in two separate processes asynchronously using a thread mechanism.

In the process of force computation, collision between the object and the plane is detected, interaction force is computed, and history of force is updated. The computa-tion is performed at an interval of 2 ms. The process of deformation computation refers to the history of force and computes the deformation of the entire model.

4.3 Experimental Result

An example of interaction with the model is shown in figure 5. The model is rolling over a floor; intensity of force that was computed between the model and the floor is also shown in Figure 6.

(a) t=0 t=88 T=96 t=104 t=112 t=120 t=128ms

(b) t=0 t=88 T=96 t=104 t=112 t=120 t=128ms

Fig. 5. Example of interaction

0

10

20

30

40

50

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14Time (s)

For

ce (

N)

Fig. 6. Interaction force

5 Conclusion

In this paper, an extension of impulse response deformation model was discussed. As an approach to efficient computation of interaction causing surface contact, a concept of

680 K. Tagawa, K. Hirota, and M. Hirose

virtual degree of freedom was proposed. Through implementation of a prototype system and experiments using the system, the approach was proved to work effectively.

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