Haptic Rendering of Virtual Hand with Force Smoothing

Miao Feng, Jiting Li, Member, IEEE, Ruoyin Zheng State Key Laboratory of Virtual Reality Technology and Systems

Beihang University Beijing, China

miaofeng@me.buaa.edu.cn, lijiting@buaa.edu.cn, ryzheng860909@126.com

Abstract—In this paper, we present methods to generate a stable and realistic force rendering between virtual hand and object for a hand rehabilitation system. There are multi-contact regions between hand and object. For each contact region, the virtual contact force is modeled upon the spring-mass model. As direct rendering with spring-mass model in a large stiffness will induce instability of the haptic device, we apply a force-smoothing method by limiting the maximum force variation to guarantee the stability in the haptic rendering. The system experiment results demonstrate that the proposed method can provide satisfactory stable haptic display. And the maximum virtual stiffness that the system can simulate increases from 0.7 N/mm to 1.6N/mm by using force smoothing process.

Keywords-Haptic Rendering; Force Smoothing; Stability; Virtual Reality; Hand Rehabilitation

I. INTRODUCTION The human hand provides an important interface to the

physical world. In the virtual rehabilitation system of human hand, the virtual hand, as the avatar of the human hand, provides a natural interface to the computer synthesized virtual world. Therefore, the haptic modeling of the virtual hand plays an important role to accomplish the fidelity of the hand-object interaction. In the past decades, the virtual hand modeling and hand-object interaction have been investigated widely to meet the needs in various applications [1]-[7]. Most of them used the penality-based methods to compute the force feedback in the hand-object interaction [1]-[6]. Burdea’s team and Huagen Wan computed the reactive hand force by using the mass-spring system with the Hooke’s Law [1][2]. And Burdea’s team used the force direction smooth processing method to avoid the large variation in the force display[1]. In [3], the stiffness and viscosity coefficient of object were considered to generate the hand force feedback according to the inter-penetration. Kron and Ott used the mass-spring-damping system to compute the force feedback on hand [4][5]. Cui used the nonlinear Duffing Equation to calculate the contact force [6]. In Stepp’s force model, the stiffness characteristics of object were defined as two continuation piecewise functions of vertical displacement, which were consisted with a linear stiffness and cubic polynomial [7]. For an existing haptic device, its stiffness is limited. In order to improve reality in interaction simulation between rigid objects, the virtual stiffness should be as high

as possible. But if the virtual stiffness is larger than the stiffness that the haptic device can afford, the system may be unstable. Few papers mentioned above have paid attention to how to improve the virtual stiffness that the system can simulate. According to Luecke’s work, in mass-spring-damping model, high stiffness alone usually causes noticeable oscillations, and adding damping can prevent this oscillations. However, the addition of large amounts of damping can cause high frequency vibration during contact [8].

In this paper, we investigate the force rendering of hand-object interaction for the virtual rehabilitation system of human hand. We propose a penalty-based virtual force model with Hooke’s law. A simple but effective force smoothing method is introduced to realize a higher virtual stiffness in order to improve fidelity in rigid objects interaction simulation, as well as to ensure the system be stable. This method can notably improve the maximum virtual stiffness of our system.

The rest parts of this paper are arranged as follows. We commence with the introduction of the virtual hand model in Section II. We subsequently propose haptic rendering of virtual hand interaction with rigid object, including virtual force modeling and force smoothing process, in section III. The experiments are conducted in section IV. The conclusion of our investigation is discussed in section V.

II. VIRTUAL HAND MODEL As shown in Figure1, the virtual hand is simplified as

five digits and a palm, with three segments for each digit. Except the thumb, the other four fingers have the same kinematic structures, i.e., with three phalanges, which are distal, medial, and proximal phalanges, and three joints, which are the distal interphalangeal (DIP) joint, proximal interphalangeal (PIP) joint, and the metacarpophalangeal (MCP) joint. Likewise, the thumb has three phalanges, which are distal, proximal, and metacarpal phalanges, and three joints, which are the interphalangeal (IP) joint, metacarpophalangeal (MCP) joint and carpometacarpal (CMC) joint. The DIP, IP, PIP and thumb’s MCP joints are modeled as one-Degree-Of-Freedom (DOF) hinges to realize the flexion/extension motions, while the two-DOF MCP joint of index finger and CMC joint of thumb are simplified as two one-DOF hinges with orthogonal and intercrossing

2011 International Conference on Virtual Reality and Visualization

978-0-7695-4602-5/11 $26.00 © 2011 IEEE

DOI 10.1109/ICVRV.2011.11

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rotating axis to realize the corresponding motions of flexion/extension and adduction/abduction.

Figure 1. The virtual hand model

With this kinematic structure, the virtual hand can grasp the object with any part, i.e., any segment of any digit, which is consistent with the human hand grasp.

III. HAPTIC RENDERING We confine our simulation task in the static grasping

domain, which refers to as the contact between fingers and the object occurs at fixed points, without sliding or rolling of phalanges over the object.

A. Virtual Force Model In the following parts, for description simplicity, we use

the abbreviation GDP for graphic display position, and HCP for haptic device controlled position. We determine the GDP to the position at which the contacts happen, which is described in [9].

In the interaction between hand and object, there is no more than one contact point on each segment. For each contact point GDPi, the virtual contact force is modeled upon the spring-mass model and calculated with Hooke's law.

i i ik d= ⋅ ⋅F n (1) ,i GDPi HCPid = d (2)

where Fi is the contact force at the contact point GDPi; k

represents the virtual stiffness coefficient; id is the penetration depth at contact point GDPi; ni is the normal of object at the contact point GDPi; dGDPi,HCPi is the penetration depth vector from GDPi to HCPi, as shown in figure 2.

Figure 2. The virtual contact force rendering

B. Force Smoothing For Large Stiffness For a given haptic device, its stability is typically limited

by the maximum stiffness of the spring force model. With a small virtual stiffness, the system is stable but the penetration between hand and object is too large to generate an acceptable fidelity in rigid interaction simulation, especially in power grasp simulation. However, increasing the virtual stiffness will cause big vibration in force feedback. And the big fluctuation of force feedback will cause system unstable and terrible vibration of the device. So we used a force-smoothing process to avoid large fluctuation of force value in order to ensure the system to be stable. In this method, a range of force variation [ minFΔ , maxFΔ ] is confirmed to limit the variation of virtual force value in each time step. minFΔ is a negative value limit force quantity of decrease, and maxFΔ is a positive value limit force quantity of increase. By this way, the force fluctuation can be limited, the vibration is diminished and the system is stable.

For each contact point i, the force feedback value in time

t ,i tF is determined by the formula: ,( 1) max max

, ,( 1) min max

,( 1) min min

i t i

i t i t i i

i t i

F F F FF F F F F F

F F F F

−

−

−

� + Δ Δ ≥ Δ�

= + Δ Δ ≤ Δ ≤ Δ�� + Δ Δ ≤ Δ� (3)

,( 1)i i i tF F F −Δ = − (4)

where ,( 1)i tF − is the force feedback value in the last time t-1 and iF is the value of force calculated directly by the penetration depth in time t with the Hooke’s law as (1).

If the range of [ minFΔ , maxFΔ ] are too wide, the system can’t keep stable, but with too narrow range force feedback may have hysteresis. With a suitable value of minFΔ and

maxFΔ , the system can provide stable and realistic force feedback in large virtual stiffness interaction simulation.

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IV. EXPERIMENT We executed experiments on a host computer with the

configuration of Intel Core i7 870 @ 2.93GHz CPU, 2.93 GB memory, an ATI Radeon HD5570 graphics card, and Windows XP operation system. The virtual hand is controlled by a hand exoskeleton we developed for motor capability rehabilitation of human hand Error! Reference source not found.. The hand exoskeleton is actuated by eight motors and can comply with the joint motion of the human index finger and thumb (figure 3). Each finger has four degree of freedoms to realize the corresponding motions of flexion/extension and adduction/abduction. The joint angles of the finger are measured by the angle sensors (potentiometers) and mapped to the virtual finger and thus control the virtual finger movement.

Figure 3. Hand rehabilitation system

Virtual hand and objects are constructed with triangular mesh. 2248 triangles of hand model are involved in the calculation , and 992 is the number of triangles of object model. Collision detection used in our simulation system is a fast discrete collision detection library -PQP library proposed by Ming C Lin [11]. The haptic rendering update rate is 200Hz, which is acceptable to get stable force feedback with our exoskeleton force feedback device.

The first task is to press a teapot with index finger at the virtual stiffness of 0.9N/mm. We test the simulation of force rendering without force-smoothing and with force-smoothing at a range of force variation [-0.05N, 0.05N]. And the values of contact force are presented in figure 4. We can see that without the force smoothing, the system is unstable. Contrastively, after using the force smoothing, the system is non-variation and presents a stable force feedback.

Figure 4. Press the teapot surface ((a). force rendering without force smoothing; (b). force rendering with force smoothing)

Figure 5 shows the hand-object interaction at virtual stiffness of 1.4N/mm by using force smoothing with a range of force variation [-0.1N, 0.1N] in each time step. Corresponding contact forces on phalanges are shown in the following figures. We can see that the force feedback is stable at virtual stiffness of 1.4N/mm.

(a)

(b)

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Figure 5. Force feedback of hand-object interaction at virtual stiffness of 1.4N/mm

For the characteristic of tendon-sheath transmission of our exoskeleton, the maximum virtual stiffness that the system can simulate is 0.7N/mm without force-smoothing. By using the maximum force variation limitation, the system can stably run at the virtual stiffness of 1.6N/mm. The compute cost of the force smooth process is small, which has little influence on haptic rendering update rate.

V. CONCLUSION In this paper, we present a force model for haptic

interaction in virtual hand simulation. In our approach, the forces are calculated with smooth processing by limiting force value variation each step to enhance the stability in haptic rendering and generate larger virtual stiffness. Based on these methods, we developed force rendering of hand-object interaction for hand rehabilitation. The results show that the feedback force is stable and the largest virtual stiffness that the system can simulate increases from 0.7N/mm to 1.6N/mm by using force smoothing. This work demonstrates that our force smoothing method is effective in eliminating vibration in larger stiffness simulation, thus improving the stability of the system.

ACKNOWLEDGMENT

This work is supported by the National Natural Science Foundation of China under the grant No. 50975009, and by the research project of State Key Lab of Virtual Reality Technology and Systems of China.

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