Two typical examples are Stanford/JPL hand. [10] that has 3 fingers with 9 degrees of freedom (DOF), and Utah/MIT hand [4] which has 4 fingers with 16 DOF.
On the Design of a Novel Dexterous Hand W.J. Chen and M. Xie School of Mechanical and Production Engineering Nanyang Technological University Republic of Singapore 639798
Abstract This paper addresses the design and development of a single-motor-driven dexterous hand. The hand possesses the following characteristics: (1) single electric actuator mechanism for multi-DOF’s through the use of clutches, (2) modular structure to support reconfigurability, and (3) cable-driven system to allow remote location of the actuator. Due to these features, the hand is able to provide a wide range of ability for various grasping and manipulation. In addition, the paper also conducts the kinematics analysis and develops an algorithm of torque calculation for the hand’s control system modeling. Key words: Multi-fingered hand, service robot, grasping
1
Introduction
A service robot (see Fig. 1) is currently under construction in the Robotics Research Center at the Nanyang Technological University to meet increasing demand in material handling and service area [5]. As one of key components of the robot, a multi-finger dexterous hand is being keen required. It is hoped to perform the fine manipulation and grasping, as well as to reconfigure itself easily for different tasks. To obtain enough dexterity, multiple DOFs are required for a robot hand. Normally, one DOF needs an independent motor to drive its motion. Thus, a dexterous hand may have a great number of motors inside. This results in a costly budget and a difficulty in modeling of control system and design of mechanical structure [11]. It is therefore important in the design phase to integrate hand’s DOFs into the system but not to affect its function in both mechanism and control. On the other hand, it is also important that a hand has the flexibility or versatility to better adapt to the shape of object. This presents another requirement on the design of hand’s construction for achieving the re-configurable feature easily. A number of multi-fingered hands [3, 4, 8, 10] have been developed in the world so far. Most of them use an anthropomorphic configuration with tendon-driven mechanism. Two typical examples are Stanford/JPL hand [10] that has 3 fingers with 9 degrees of freedom (DOF), and Utah/MIT hand [4] which has 4 fingers with 16 DOF in total. These designs were aimed at emulating the properties of human hand rather than meeting the requirement of specific tasks. In parallel with the
Fig. 1. Service robot under construction
development of hand prototypes, various issues related to grasping [1], contact point friction forces [6], and control strategies [9] have also been discussed. Although these researches provide a base for design, further work is still needed to build a practical dexterous hand. In our work, an electric single actuator mechanism is designed and developed for multi-DOF motion. Also, the modular concept is applied to support reconfigurability. The actuator includes only one motor. The motion of each DOF is obtained by controlling “on” or “off” of corresponding two clutches. Each finger or phalange is an independent subsystem. Therefore, the hand can change its configuration by either extending phalange number or adding additional finger. In this way, the hand is capable of supporting a wide range of application where objects of complex shape need to be handled properly. The organization of the paper is as follows. In section 2, the design feature of the hand prototype in mechanical aspects is addressed. It is followed by a description of the control scheme in section 3. The kinematics analysis and torque calculation are given in section 4. Finally, some conclusions are remarked.
2 Physical Prototype Mechanism Description The proposed dexterous hand is shown in Fig. 2. The hand is approximately of human-hand size and is able to pick up an object with the largest dimension of 10 cm. Currently, it comprises three fingers (including one thumb) that is the least finger number for a hand to stably grasp arbitrary shape of object, but the finger number may vary if required. Each finger consists of three phalanges that are connected by three rotational joints. The palm is constructed with five aluminum plates connected with screws. The finger can be mounted on the palm directly. Through the four holes located at the rear plate in the palm, the hand can be attached to the service robot arm or other manipulators. The arrangement of fingers and palm is a compromise among workspace, compact size and the limitations imposed by tendon routing.
Fig. 2. The multi-finger dexterous hand.
Each of joints is actuated by two wires that are driven by pulleys in the actuator system (see Fig. 3). Through changing the winding manner on the pulley as shown in Fig. 3, the number of DOF of the hand is able to vary from 1 to 9 according to a required task. Due to application of the modular concept, three fingers are identical in structure and assemble. The phalanges, especially the middle phalange, in each finger are also designed according to the modular concept. In addition, the structure of all joints in the fingers is the same as well. With the special design of joints, the connection between two phalanges can be easily assembled. Thus, the link number in a finger can be extended to form a new configuration for task change. Actuator System It is difficult to house actuator and transmission unit within fingers because the finger must be compact and as light as possible. Tendon driven system permits the remote location of actuators, thereby providing a solution for reduced finger size [7]. In our work, actuators and controllers of fingers are intended to install within the service robot body where the power and main processors are interfaced. Figure 6 shows the photo picture of the actuator system used in the hand. The system consists of one motor, 18 relatively cheap and small clutches, 9 sets of worm gears (each one mounts two pulleys) and other transmission components. The construction is separated into three identical layers, which are connected to motor through timing belt. Each layer is independent and includes three sets of worm gears that drive rotation of finger joints through cables. In principle, one set of worm gears is controlled by two clutches. The motor as a unique power source always runs when any finger needs motion. Through “on” or “off” of two clutches, the power of motor can be transmitted to each joint. Thus, the system outputs 9 independent motion totally.
(a)
joint
Outer cable
(b)
tendon joint
Outer cable
spring
(c) tendo n
spring
(d)
Fig. 3. DOF change in two joints, (1) using cases (a) or (b) , two DOFs; (2) using cases (c) or (d), one DOF.
Fig. 4. Actuator system driven by one motor.
Design Features Two major design features make the hand different from the other existing hands. Firstly, unlike Stanford/JPL hand or Utah/MIT hand, multi-DOFs here are actuated by a single actuator mechanism. Since the motion component such as clutch is relatively cheap and small, the hand is cost-effective. Secondly, the hand is reliable and can be easily reconfigured due to its modular structure. The modular characteristics are reflected not only in fingers also in actuator. Three finger modules can be independently pre-assembled and tested, and then put together to form a desired hand configuration.
reaction force F output
input finger tip
θ
desired Force actuator
controller desired position
Fig. 6. Block diagram of force and position control of fingers.
τ
3 Control Scheme
T1
Since the whole service robot (including two hands) comprises a large number of DOFs, a distribution control system is applied. The whole system is divided into five modules, each of them has a sub-CPU to independently process their own task such as motion planning, torque computation, etc. The main CPU has the main role to process the data from vision system as well as to coordinate the motion of inter-modules. In the hand stage, a micro-controller controls the finger motion. Below a possible hand control scheme is discussed. The control architecture of the hand includes two levels as shown in Fig. 5. In the high level, the finger motion and pre-shape planing will be done through integrating vision information from the main CPU. In the low level, a force and position control is executed in the micro-processor 68HC11 to control joint motion (see Fig. 6). In this level, the reaction force information is obtained through torque detection by virtue of Jacobian matrix. Joint torque is obtained from measuring the wire’s tension by using strain gauges. The measuring method is shown in Fig. 7. The position control of each joint is executed with openloop. Home positions of joints are recognized by using limit switches.
Vision data processor
High Level
Database
Motion Planning
T2
τ = (T1-T2)r
(b)
(a)
Fig. 7. Measuring method of joint torque, (a). measure wire tension, (b) calculate torque. The motion transmission through clutch from motor (input) to worm gear (output) can be schematically shown in Fig. 8. The rotation direction of output depends on the shifting of “on” or “off” of a clutch couple. The angular position and velocity can be determined by:
ω = λω 0 θ = λω t where
λ=
tn is the duty factor of control signal in tp
clutches, ω and θ are angular velocity and position of worm gear respectively, ω 0 is angular velocity of motor. Thus, through controlling engaging time t of clutch and duty factor λ of input signal, we can determine joint’s motion information.
input (motor)
Motion Controller clutch
Low Level
Force and Position sensing
gear pair
digital signal
tn
output
Actuators
clutch
tp Camer a
FINGER
Fig. 5. Control architecture of the hand.
Fig. 8. Schematic chart of motion transmission through clutches.
4 Modeling and Analysis In the hand control, the shape of the grasped object is determined by the vision system and the hand’s task planning in task space is determined in the high level. The objective of hand mechanics analysis is to find the relationship between joint space and task space of hand as well as to determine joint forces in order to facilitate force and position and/or velocity control in the low level. Kinematics Analysis Since all fingers are identical, only one finger module is discussed in analysis. In Fig. 9, {H} and {F} denote the palm frame and finger frame respectively. The frame {F} is fixed at the axis of joint 1, therefore the motion of finger with respect to the frame is within the plane called finger plane. The position of contact point P relative to the {F}, (Fxp,, Fyp, Fzp)T, can be expressed by joint variables as:
F x p = l1 + l 2 cosθ 2 + l3 cos(θ 2 − θ 3 ) F , yp = 0 F z p = l 2 sin θ 2 − l 3 sin(θ 2 − θ 3 )
(1)
Mapped to {H}, the position of point P, (Hxp, Hyp Hzp)T, is
H x p cθ 1 H y p = sθ 1 H z p 0
0 F x p H x F 0 F y p − H y F (2) 1 F z p H z F
− sθ 1 cθ 1 0
where (HxF, HyF, HzF)T are the coordinates of the origin of {F} with respect to {H}. Eqs (1) and (2) give the transformation from joint space to task space (forward kinematics). Inverse transformation (inverse kinematics), i.e. from task space to joint space, can be obtained by F F y x θ1 = tan−1 F p , η = p − l1 xp cosθ1
l +η2 +Fz2p − l32
η − tan−1( F ) zp
2 −1 2
θ2 = cos
2l2 η + z
2 F 2 p
θ3 =π − cos−1
l32 + l22 − (η2 +Fz2p )
Joint Torque Computation Referring to Fig. 10 for a three-finger hand with a stable grasping, the external and internal force and moment must satisfy the following equilibrium equation and friction constraints. These can be expressed as:
F = Af
(3)
f iT e i 1 ≥ fi 1 + µ i2
, i =1,2,3
(4)
where F ∈ ℜ 6×1 is the generalized external force vector;
A ∈ ℜ 6×9 is grasping matrix with the form E A= R1
E R2
0 E 6×9 = , R ∈ ℜ i riz R 3 − riy
− riz 0 rix
E ∈ ℜ 3×3 is unit matrix; f i ∈ ℜ 3×1 is contact (or grasping)
force vector and f = [f1 f 2 f 3 ]T ∈ ℜ 9×1 ; ei is the normal vector of the tangent surface at contact point; and µ is the friction coefficient. Once the force vector f satisfying Eqs (3) and (4) is obtained, the joint torque of the finger can be calculated by:
τi = J
T i fi
(5)
where τi ∈ ℜ 3×1 is torque vector of finger-i, and Ji is Jacobian matrix from joint space to {H} with the form: − (l3c(θ 2 −θ 3 ) + l2 cθ 2 + l1 )sθ1 (−l3 s(θ 2 −θ 3 ) − l 2 sθ 2 )cθ1 l3cθ1 s(θ 2 −θ 3 ) J = (l3c(θ 2 −θ 3 ) + l 2 cθ 2 + l1 )cθ1 (−l3 s(θ 2 −θ 3 ) − l2 sθ 2 )sθ1 l3 sθ1s(θ 2 −θ 3 ) 0 − l3c(θ 2 −θ 3 ) l3 c(θ 2 +θ 3 ) + l 2 cθ 2
Note that Eq. (3) is redundant, and the friction constraints expressed by Eq. (4) are non-linear. Clearly, solving such problem with conventional optimal approaches will be time-consuming. To consider effectively the nonlinear nature of friction forces at contact point, an approximate optimal method presented in [2] can be applied. It allows us to incorporate the observed characteristics of the optimal force distribution into a more direct and computationally efficient method for the force distribution.
2l2l3
Pθ 3
{T}
l3
θ2
l2
fi
Z X
{H}
{F}
ri
l1
F
Y
Palm
θ1
Fig. 9. Geometry of a finger module.
riy − rix 0
{H}
Fig. 10. A hand-object system.
We express the grasping force f as a sum of forces at desired value f0 and small deviations, fp: f = f0 + fp (6) Substituting (6) into (3) yields: F − Af 0 = Af p
At present, the prototype of the hand has been built. The control strategies (including grasping strategy, slipping and tactile detection studies) and full algorithm implementation are being on the way. It is our hope to complete an intelligent dexterous hand as soon as possible.
(7)
The nonlinear constraints can be expressed as a vector of nonlinear homogeneous equation [2] as shown below g (f ) = 0 (8) where g could be a vector of functions of length 1 to 3. Eq. (8) can be linearized at f0 as below:
g i (f ) = g i (f 0 ) + g i1 f 1p + g i 2 f 2 p + ⋅ ⋅ ⋅ + g i ,9 f 9,p = 0 where g ij =
∂g i ∂f j
are the coefficients. We can now write
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M.R. Cutkosky, Robotic grasping and fine manipulation, Kluwer Academic Publisher, 1985.
[2]
J.F. Gardner, “Efficient computation of force distributions for walking machine on rough terrain.” Robotica, Vol.10, pp. 427-433, 1992
[3]
H. Hashimoto, et al. “A multi-finger hand with newly developed tactile sensor,” J. of Robotics and mechatronics Vol.5, No.1, pp. 60-64, 1993.
[4]
S.C. Jacobsen, et al., "The Utah/MIT dexterous hand: Work in process.” The Int. J. Robotics Research 4(3), pp. 21-50, 1984.
[5]
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[6]
H. Kobayashi, “Control and geometrical consideration for an articulated robot hand,” Int. J. of Robotics Research, Vol.4, No.1, pp. 3-12, 1985.
[7]
H. Kobayashi et al. "On tendon-driven robotic mechanisms with redundant tendons, " The Int. J. of Robotics Research, Vol.17, No.5, pp561-571, 1998.
[8]
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[9]
T. Oomichi, et al. "mechanics and multiple sensory bilateral control of a fingered manipulator," 4th Int. Symp. On Robotics Research, MIT Press, pp. 145153, 1987.
f0
the nonlinear constraints in terms of f0 and fp in the following matrix form: −g(f 0 ) = Hf p
(9)
where H is a matrix composed by the coefficients gij. Combining Eqs. (7) and (9) yields: F − Af 0 A - g (f ) = f p 0 H
(10)
By now the approximate optimal grasping force distribution can be computed as follows: 1 2
3 4 5
Choose a starting point, f0 which may or may not satisfy Eqs. (3) and (4). Compute the 9×1 vector fp. If the norm of this vector is less than the convergence tolerance, then exit. Compute the linearized coefficients, H. Solve Eq. (10) for corrections of the force. Update the force using (6) and go to step 2.
5 Conclusion This paper presents the work on design of a novel dexterous hand, including the structure of fingers, the actuation system, and the control system as well as the details of kinematics and joint torque calculation. Primary objective of such a design is to provide the hand with a cost-effective function and a reconfigurable ability for different tasks. The developed solution is based on a proper modular design of finger structures and the use of a single-motor-driven actuation system. The hand is currently intended to be an appendage of a service robot to extend the robot’s service functions. Due to its special feature, the dexterous hand may also be applied to areas such as flexible manufacturing lines, and material handling in space or hazardous environment.
[10] J.K. Salisbury and J.J. Craig, “Articulated hands: Force control and kinematic issues,” International Journal of Robotics Research, 1(1), pp. 4-17, 1982. [11] Jichuan Zhang, et al. “Optimal design of a six-bar linkage for an anthropomorphic three-jointed finger mechanism,” DE-Vol. 45, Robotics, Spatial Mechanisms and Mechanical Systems, ASME, pp.149-154, 1992.
