Analysis of Coordinated Motions of Humanoid Robot Fingers Using Interphalangeal Joint Coordination

Abstract

In this study, we analyse the coordinated motions of humanoid robot fingers using an interphalangeal joint coordination. For this purpose, four humanoid robot fingers with different sizes have been considered. A biomimetic interphalangeal joint coordination (IJC) formulation based on the grasp configuration of human fingers has been presented for humanoid robot fingers. The usefulness of the specified IJC formulation for human-like finger motion has been verified through comparative demonstrations. As a result, a proper coordination of humanoid robot fingertips can be achieved by applying our IJC formulation. Also the IJC formulation can be used to design of humanoid robot fingers.

Keywords

Interphalangeal Joint Coordination Human-like Finger Motion Humanoid Robot Fingers

1. Introduction

A dexterous multi-fingered robot hand is required for achieving the performance of intelligent humanoid robots [1][2]. To develop such a robot hand, a lot of valuable researches have been performed [3]–[6]. Some researchers attempted to mimic the skills of human hands for dexterous humanoid robotic and prosthetic hands [7]–[9]. In this research direction, the effort of identifying the joint motion behaviors of human fingers is important for effective human-like motions [10][11].

To achieve the desired dexterity of an object manipulation, it is important to manage the joint configuration of a finger in a preferable manner according to the purpose of given task, and coordination of multiple fingers is also required. Related to such a finger configuration, many researches have been performed in terms of singular configuration, redundancy, or obstacle avoidance issues in robotic applications [12][13]. From a biomimetic viewpoint, a few researches have been put forth for characterizing the joint relationship in a human finger [14][10]. In addition, a joint combination has been considered for the motion planning of a prosthetic finger, where the third joint of the finger is suggested to be actuated identically according to the motion of the second joint [15]. This approach is somewhat interesting for a simplified robotic finger motion. Since the motion ranges of those joints in human fingers are actually not identical [10][16], however, Secco's approach [15] may not be implemented for human-like motions of humanoid robot fingers or prosthetic fingers. In the same line of research, we attempted to identify the feasible interphalangeal joint coordinations of human fingers while grasping [11], and planned a human-like finger motion considering the joint coordination [17]. However, the coordinated motions of humanoid robot fingers while grasping are not analysed thoroughly yet in the aforementioned approaches.

The objective of this study is to provide an interphalangeal joint coordination method for effective human-like motions of humanoid robot fingers and analyse its usefulness. This paper is organized as follows. In Section 2, we reveal the coordinated motion behaviors of human fingers and describe a useful interphalangeal joint coordination formulation of humanoid robot fingers. In Section 3, the usefulness of the formulation is verified through comparative demonstrations. In addition, coordinated human-like motion and effective design of humanoid robot fingers using an interphalangeal joint coordination are discussed. Concluding remarks are finally drawn in Section 4.

2. Biomimetic Formulation of IJC of Humanoid Robot Fingers

In this section, we reveal the fundamental coordinated motion behaviors of human fingers and describe a formulation to effectively determine an interphalangeal joint coordination of humanoid robot fingers.

2.1 Coordinated Motions of Human Fingers

Consider the skeletal configuration of human hand shown in Figure 1. In general, the human hand consists of the thumb and four fingers, and totally there exist five metacarpals and fourteen phalanges [18] [19]. Each of the four fingers consists of one metacarpal and three phalanges such as proximal, middle, and distal, whereas the thumb has one metacarpal and two phalanges, proximal and distal. Those phalanges become progressively smaller from proximal to distal. The MCP(MetaCarpoPhalangeal) joint plays a role of the base for the actuation of each finger. The joints between the phalanges are called interphalangeal joints. Each finger has two interphalangeal joints, PIP(Proximal InterPhalangeal) and DIP(Distal InterPhalangeal), and the thumb has only one.

Figure 1.

Skeletal configuration of human hand

According to the literatures [18] [19], it is known that the human fingers utilize the appropriate joint coordination between the PIP joint and the DIP joint. Such a joint coordination-based robotic finger motion is called a human-like finger motion in this paper. Some researchers tried to find the feature of such a joint relationship of human fingers [10] [16]. In the viewpoint of robotic applications, we also attempted to identify any feasible relationship among the joint motions of human fingers through experimental works for iterative reach-to-grasp movements of fingers [11]. Through the experiment, we confirmed that there exists a linearizable interphalangeal joint coordination between the PIP joint and the DIP joint of each human finger, but its coordination parameter is different in the iterative reach-to-grasp movements. Actually, we can experience that the DIP joint is actuated dependently according to the motion of the PIP joint in our finger motions. Also, we can observe empirically that a proper coordination of multiple fingers is used for general object manipulation tasks.

Thus, in terms of biomimetic applications, it can be fascinating to utilize such interphalangeal joint coordinations of human fingers for human-like coordinated motions of humanoid robot fingers.

2.2 Formulation of IJC of Humanoid Robot Fingers

Figure 2 shows some exemplary configurations of a humanoid robot finger during grasping. Actually, such finger configurations can be experienced in a reach-to-grasp movement of human fingers. If we apply the coordinated motion behavior of a human finger to the humanoid robot finger shown in Figure 2, the joint relationship between the PIP joint and the DIP joint of the ith humanoid robot finger can be expressed approximately as follows:

θ_{3 i} = λ_{i} θ_{2 i}

(1)

where the issue is how to effectively assign the interphalangeal joint coordination (IJC) parameter λ_i.

Figure 2.

Exemplary configurations of an i-th humanoid robot finger during grasping

To devise a formulation for such an IJC parameter, we carefully observed the grasping and manipulating configurations of human fingers, as shown in Figure 2, and reconsidered the previous research [11]. Thus, the following two extreme postures of the humanoid robot finger have been considered simply for the formulation. One is the maximum flexion posture, as shown in Figure 2(a). The other is the maximum extension posture, as shown in Figure 2(c). If the PIP and DIP joints initially moves from the maximum extension posture to the maximum flexion posture, their movements are at maximum. If the movement of the humanoid robot finger is to mimic the behavior of a human finger, the motion of the DIP joint is basically planned by considering the joint coordination in (1). Also, a consistent coordination of all fingers is required for effective human-like finger motions.

In this sense, to determine the IJC parameter of the ith humanoid robot finger in Figure 2, we present the following formulation:

λ_{i} = \frac{Δ θ_{3 i}}{Δ θ_{2 i}}

(2)

where Δθ_3i(= θ_3i,max − θ_3i,min) and Δθ_2i (= θ_2i,max − θ_2i,min) imply the motion ranges of the DIP and PIP joints, respectively. Here, θ_2i,max, θ_2i,min, θ_3i,max, and θ_3i,min denote the maximum and minimum motion angles of the PIP and DIP joints of the ith humanoid robot finger, respectively. The angles of θ_2i,min and θ_3i,min have been assigned as a reference angle of 0 degree by observing the motion limits of human fingers, respectively.

In order to assign the maximum motion angles in (2), a triangular maximum flexion posture, as shown in Figure 2(a), has been considered. Then, the maximum angles of the PIP and DIP joints of the finger can be obtained as follows:

θ_{2 i, m a x} {= 180}^{o} - α_{i}

(3)

θ_{3 i, m a x} {= 180}^{o} - β_{i}

(4)

where the angles of α and β are determined by

α_{i} = \cos^{- 1} {\frac{{(l_{1 i})}^{2} + {(l_{2 i})}^{2} - {(l_{3 i})}^{2}}{2 l_{1 i} l_{2 i}}}

(5)

β_{i} = \cos^{- 1} {\frac{{(l_{2 i})}^{2} + {(l_{3 i})}^{2} - {(l_{1 i})}^{2}}{2 l_{2 i} l_{3 i}}} .

(6)

By considering the kinematic feature of human fingers, the sizes of phalanges of the ith humanoid robot finger in (5) and (6) are necessary to satisfy the following conditions:

l_{3 i} < l_{2 i} < l_{1 i}

(7)

l_{1 i} < (l_{3 i} + l_{2 i}) .

(8)

If the ith humanoid robot finger satisfies the conditions in (7) and (8), the maximum angle of the distal interphalangeal joint is usually less than the maximum angle of the proximal interphalangeal joint so that λ_i < 1.0. It is also remarkable that the procedure of (2)∼(8) enables us to get a consistent interphalangeal joint coordination parameter even if the size of the humanoid robot finger is different. In the next section, we attempt to verify the usefulness of our IJC formulation and demonstrate the coordinated motions of humanoid robot fingers using such an interphalangeal joint coordination.

3. Comparative Demonstration: Coordinated Motions of Humanoid Robot Fingers

The goal of this section is to verify the usefulness of our IJC formulation through comparative demonstrations for the coordinated motions of humanoid robot fingers.

For this purpose, we considered a humanoid robot hand with four fingers as shown in Figure 3, and performed exemplary simulations for the four fingers to form the maximum flexion posture, as shown in Figure 2(a). For effective demonstration, the trajectories of the MCP and PIP joints of the ith humanoid robot finger have been predefined as follows:

θ_{1 i} = θ_{1 i, m a x} \sin (0.5 π t / t_{f})

(9)

θ_{2 i} = θ_{2 i, m a x} \sin (0.5 π t / t_{f})

(10)

where the final time parameter t_f has been set as 2.0 s. Then, the resultant trajectory of the DIP joint (θ_3i) of the ith finger is simultaneously determined by (1).

Figure 3.

A four-fingered humanoid robot hand: (a) front view and (b) side view.

In order to analyse the coordinated motions of humanoid robot fingers, we employed our IJC formulation and the Secco's approach [15] and attempted to compare the patterns of the actual fingertip trajectories for the flexion motion. The actual fingertip trajectories have been obtained by using the predefined joint angles as follows:

x_{f i} = l_{1 i} c_{1 i} + l_{2 i} c_{1 i 2 i} + l_{3 i} c_{1 i 2 i 3 i}

(11)

y_{f i} = l_{1 i} s_{1 i} + l_{2 i} s_{1 i 2 i} + l_{3 i} s_{1 i 2 i 3 i}

(12)

where x_fi and y_fi denote the x- and y-directional positions of each fingertip, as shown in Figure 3(b), respectively. The parameter l_ji represents the length of the jth link of the ith finger. The parameters abbreviated for effective description have been defined as follows; s_1i = sin(θ_1i), s_1i2i = sin(θ_1i + θ_2i), s_1i2i3i = sin(θ_1i + θ_2i + θ_3i), c_1i = cos(θ_1i), c_1i2i = cos(θ_1i + θ_2i), and c_1i2i3i = cos(θ_1i + θ_2i + θ_3i).

3.1 Coordination of Four-fingered Grasping

The objective of the first simulation is to analyse the coordinated motions of the above-mentioned four-fingered humanoid robotic grasping by employing our IJC formulation and the Secco's approach.

In the first simulation, we used the specifications of the humanoid robot fingers indicated in Table 1, where λ_i has been determined by (2)∼(8). Actually, the phalangeal length parameters of the fingers have been assigned by considering the normal size of human fingers, l_T4 < l_T1 < l_T3 < l_T2, and the conditions in (7) and (8). In Table 2, the maximum motion range of the MCP joint (θ_1,max) has been assigned empirically, and the others have been determined by (3) ∼ (8). The joint trajectories of the humanoid robot fingers predefined for the maximum flexion motion have been plotted in Figure 4.

Figure 4.

Joint trajectories of the humanoid robot fingers predefined for a flexion motion: (a) MCP joint, (b) PIP joint, and (c) DIP joint.

Table 1.

Phalangeal parameters assigned for humanoid robot fingers

i	Finger	Length of phalanx (m)			Total (m)	IJC λ_i
i	Finger	l _1i	l _2i	l _3i	l _Ti	IJC λ_i
1	Index	0.050	0.045	0.025	0.1200	0.6252
2	Middle	0.058	0.052	0.028	0.1380	0.6115
3	Ring	0.055	0.052	0.025	0.1320	0.6314
4	Little	0.045	0.040	0.022	0.1070	0.6098

Table 2.

Maximum motion ranges of joints of humanoid robot fingers

i	Finger	Maximum joint motion range (°)
i	Finger	θ_1i,max	θ_2i,max	θ_3i,max
1	Index	90	150.0736	93.8226
2	Middle	90	151.1629	92.4405
3	Ring	90	153.1647	96.7146
4	Little	90	150.7505	91.9211

Figures 5(a), 6(a), 7(a), and 8(a) show the traces of finger configurations of the humanoid robot fingers while flexing by employing our IJC formulation. Actually, each fingertip moves from the initial extension posture (E) to the maximum flexion posture (F) with respect to the origin of the MCP joint. As shown in Table 1, the dimensions of all fingers are slightly different from each other. Nevertheless, in the case of using our formulation, we can see from Figure 5(a)∼Figure 8(a) that a consistent closed-loop grasping posture has been formed by the trace of each finger.

Figure 5.

Finger configurations of the index finger for the flexion motion

Figure 6.

Finger configurations of the middle finger for the flexion motion

Figure 7.

Finger configurations of the ring finger for the flexion motion

Figure 8.

Finger configurations of the little finger for the flexion motion

As a comparative study, we performed the same task by changing our IJC parameters to 1.0 so that the motion of the DIP joint (θ_3i) of the ith finger is equal to the PIP joint (θ_2i). This approach was proposed by Secco, et al. [15] for a motion planning of a prosthetic finger. The resultant fingertip trajectories by using the Secco's approach have been shown in Figures 5(b), 6(b), 7(b), and 8(b). The final grasp posture compared to our formulation is quite different, and each fingertip may disturb the proximal phalanx when the motion of the PIP joint increases a little more.

In addition, Figure 9(a) and Figure 9(b) show the fingertip trajectories of the four humanoid robot fingers for the flexion motion by employing our formulation and the Secco's approach, respectively. The mark O_1i in these figures indicates the origin of the MCP joint of the ith finger, and each fingertip moves from the initial extension posture (E) to the maximum flexion posture (F). These trajectories actually have been obtained by (11) and (12) using the joint angles predefined. Of course, the corresponding interphalangeal joint coordination parameter between the PIP joint and the DIP joint is used for each fingertip trajectory. From Figure 9(a), we can confirm that all fingertip trajectories have been well-coordinated in the process of forming the maximum flexion posture by employing our formulation. In the case of using the Secco's approach, however, the coordination of all fingertips is not good. This implies that the Secco's approach may lead to difficulties in planning a human-like motion of a humanoid robot finger or a prosthetic finger [16] [20]. Therefore, our interphalangeal joint coordination formulation can be applied for effective coordination of humanoid robot fingers.

Figure 9.

Fingertip trajectories of the humanoid robot fingers for the flexion motion: (i) index finger, (ii) middle finger, (iii) ring finger, and (iv) little finger

3.2 Coordination of Finger By Modification of Size

The second simulation is to confirm the trend of relative coordination of a humanoid robot finger when its size is adjusted.

The parameters in Table 3 and Table 4 have been used for the exemplary verification of the coordination of the index finger and the middle finger shown in Figure 3, respectively, where λ₁ and λ₂ have been determined by (2)∼(8). Especially, the middle phalanx of each finger has been changed within the condition of (7). This effort practically considers new design of a finger, and such a change of the kinematic parameter results in the increment of the IJC parameter of each finger in this simulation. Thus, the actual DIP joint movement of each finger for the same flexion motion is to be increased.

Table 3.
Parameters assigned for the index finger

Case Length of phalanx (m) Total (m) IJC λ₁

l ₁₁ l ₂₁ l ₃₁ l _T1

1 0.050 0.045 0.025 0.1200 0.6252

2 0.050 0.047 0.025 0.122 0.6530

3 0.050 0.049 0.025 0.124 0.6792

Case	Length of phalanx (m)	Total (m)	IJC λ₁
1	0.050	0.045	0.025	0.1200	0.6252
2	0.050	0.047	0.025	0.122	0.6530
3	0.050	0.049	0.025	0.124	0.6792

Table 4.

Parameters assigned for the middle finger

Case	Length of phalanx (m)			Total (m)	IJC λ₂
Case	l ₁₂	l ₂₂	l ₃₂	l _T2	IJC λ₂
1	0.058	0.052	0.028	0.1380	0.6115
2	0.058	0.054	0.028	0.140	0.6369
3	0.058	0.056	0.028	0.142	0.6609

Figure 10 shows the fingertip trajectories of the index finger for the three cases of the flexion motion considering the change of the middle phalanx's size. Even though the size of the index finger has been changed, we can confirm from Figure 10(a) that the index fingertip's trajectories are well-coordinated to the other trajectories while flexing. However, the fingertip trajectories shown in Figure 10(b) do not maintain consistency and each trajectory is actually moving regardless of coordination with others. If the clearance of the middle phalanx's size specified in Table 3 and Table 4 is more larger, the patterns of the fingertip trajectories shown in Figure 10(b) and Figure 11(b) are to disperse much more. In fact, this phenomenon may cause a trouble in an object grasp and manipulation. The coordination of the middle finger by modification of the size shows a similar trend as the case of the index finger.

Figure 10.

Fingertip trajectories of the index finger for the flexion motion as follows: (i) case 1, (ii) case 2, and (iii) case 3

Figure 11.

Fingertip trajectories of the middle finger for the flexion motion as follows: (i) case 1, (ii) case 2, and (iii) case 3

As a result, consistent coordination of each finger is available by our approach even if the size of the humanoid robot finger is different, and thus we can change appropriately a corresponding fingertip trajectory so that the overall shape of the trajectories of humanoid robot fingers is similar to the pattern of human fingers. The corresponding IJC parameter can be utilized for the purpose.

3.3 Discussion

Through the above simulations, the applicability of our interphalangeal joint coordination formulation has been verified. In fact, if the human finger's IJC feature is employed for the motion planning or control of a humanoid robot finger, the movement of the humanoid robot finger is to be similar to the behavior of a human finger. From the results of the four-fingered grasping for a flexion posture, we can say that our IJC formulation is relatively appropriate for a reasonable human-like trajectory planning of humanoid robot fingers. Even though the dimension of each finger is changed, our formulation can be applied consistently for a proper coordination of fingertip trajectories. This fact is very useful for us to effectively determine the kinematic parameters of humanoid robot fingers. Also, a lot of configurations of a humanoid robot finger can be considered by adjusting the level of the corresponding interphalangeal joint coordination.

Since our IJC formulation considers the phalangeal geometry, it is practically useful for maintaining effective coordination of humanoid fingers with different sizes, and thus it plays an important role to achieve a stable grasp in terms of kinematic coordination and ultimately good performance of manipulating an object. On the other hand, the Secco's approach may not be applicable for a human-like grasp requiring precise multi-fingered coordination. The current analysis is not related to the thumb which has no any interphalangeal joint coordination.

Thus, it is remarked that our IJC formulation can be applied for effective generation of human-like finger motions. Furthermore, our approach can be used for effective design of humanoid robot fingers [2][21].

4. Concluding Remarks

The main conclusion of this study is that the coordinated motions of humanoid robot fingers can be effectively achieved by using the proposed interphalangeal joint coordination formulation. Through the exemplary simulations using flexing motions of humanoid robot fingers, we demonstrated the effectiveness of our IJC formulation. Additionally, coordinated human-like motions of humanoid robot fingers with different sizes have been analysed. We finally concluded that our IJC formulation can be applied to modulate coordinated fingertip trajectories of humanoid robot fingers as well as prosthetic fingers, and also our formulation can contribute to planning human-like finger motions. In addition, it can be applied to the design of humanoid robot fingers for ensuring effective human-like manipulating tasks.

Footnotes

5.

This research was supported by Kyungsung University Research Grants in 2014.

References

Hirai

Hirose

Haikawa

Takenaka

(1998) The development of Honda humanoid robot. Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 1321–1326.

Diamond

Knight

Devereux

Holland

(2012) Anthropomimetic robots: concept, construction and modelling. Int. Jour. of Advanced Robotic Systems, 9: 1–14.

Jacobsen

Iversen

Knutti

Jhonson

Biggers

(1986) Design of the Utah/MIT dextrous hand. Proc. 1986 IEEE Int. Conf. on Robotics and Automation, pp. 1520–1532.

Lovchik

C. S.

Diftler

M. A

(1999) The Robonaut Hand: A dexterous robot hand for space. Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 907–912.

Pons

J. L.

Ceres

Pfeiffer

(1999) Multifingered dexterous robotics hand design and control: a review. Robotica, 17: 661–674.

Butterfass

Grebenstein

Liu

Hirzinger

(2001) DLR-Hand II: Next generation of destrous robot hand. Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 109–114.

Cutkosky

M. R

(1989) On grasp choice, grasp models, and the design of hands for manufacturing tasks. IEEE Trans. on Robotics and Automation, 5(3): 269–279.

Kang

S. B.

Ikeuchi

(1997) Toward automatic robot instruction from perception-mapping human grasps to manipulator grasps. IEEE Trans. on Robotics and Automation, 13(1): 81–95.

Iberall

(1997) Human prehension and dexterous robot hands. Int. Jour. of Robotics Research, 16(3): 285–299.

10.

Hahn

Krimmer

Hradetzky

Lanz

(1995) Quantitative analysis of the linkage between the interphalangeal joints of the index finger. Jour. of Hand Surgery, 20B: 696–699.

11.

Kim

B.-H

(2006) A bio-mimetic inter-articular coordination model for humanoid grapsings. Proc. of the 2006 IEEE Int. Conf. on Robotics, Automation & Mechatronics, pp. 211–216.

12.

Yoshikawa

(1984) Analysis and control of robot manipulators with redundancy. Robotics research: the first international symposium, Eds. Brady

Paul

, Cambridge: MIT Press, pp. 735–747.

13.

Chiu

S. L

(1988) Task compatibility of manipulator postures. Int. Jour. of Robotics Research, 7(5): 13–21.

14.

Buchner

H. J.

Hines

M. J.

Hemami

(1988) A dynamic model for interphalangeal coordination. Jour. of Biomechanics, 21(6): 459–468.

15.

Secco

E. L.

Visioli

Magenes

(2004) Minimum jerk motion planning for a prothetic finger. Jour. of Robotic Systems, 21(7): 361–368.

16.

Kamper

D. G.

Cruz

E. G.

Siegel

M. P

(2003) Stereotypical fingertip trajectories during grasp. Jour. of Neurophysiology, 90: 3702–3710.

17.

Kim

B.-H

(2006) A joint motion planning based on a bio-mimetic approach for human-like finger motion. Int. Jour. of Control, Automation, and Systems, 4(2): 217–226.

18.

Watkins

(1999) Structure and function of the musculoskeletal system. Human Kinetics, pp. 74–76.

19.

Nordin

Frankel

V. H

(2001) Basic biomechanics of the musculoskeletal system, Lippincott Williams & Wilkins press, pp. 358–387.

20.

Massa

Roccella

Carrozza

M. C.

Dario

(2002) Design and development of an underactuated prosthetic hand. Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 3374–3379.

21.