Design and Experiment of an Anthropomorphic Robot Hand for Variable Grasping Stiffness

This paper introduces an anthropomorphic robot hand that has variable grasping stiffness to unknown objects without damage. The robot hand has four fingers, 13 DoFs (Degrees of Freedom) with three SEA (Series Elastic Actuator) modules in the index, middle, and ring finger. The performance for broader grasping stiffness using variable impedance control based on the parameter update block and the procedure of grasping capability evaluations of the robot hand are explained. The robot finger modules are constructed with a thumb, index, middle, and ring finger to complete the anthropomorphic type robot hand. The robot finger module has three DoFs and functions as one actuator based on an under-actuated mechanism. Additionally, external force measurement is possible in the fingertip force sensor and SEA (Series Elastic Actuator) module. For the variable impedance control implementation, a parameter update block is added to adjust the desired impedance parameter. To implement the parameter update block, we define and evaluate the correlation equation between the fingertip force, shore hardness, and damping ratio.


I. INTRODUCTION
The grasping stiffness is a parameter that must be adjusted to avoid damage when the robot hand grasps an unknown object. Humans detect elasticity with the skin and grasp objects with proper grasping stiffness [1]. Most of the research on robot hands is based on grasp taxonomy [2] proposed by Cutkosky in 1989. However, it does not consider the grasping stiffness of the robot hand, passively regulate it, or rely on the material's ductility that constitutes the robot hand. To grasp various unknown objects without damage, the grasping stiffness should be actively controlled.
For the manipulator to perform the tasks, the end-effector should be installed at the distal part to enable interaction with the object. Most end-effectors currently in use in the industry are classified into two broad categories according to task: mechanical grippers and vacuum grippers. In particular, mechanical grippers such as those shown in figure 1 are used in 2-finger type and 3-finger type grippers [3], [4]. However, The associate editor coordinating the review of this manuscript and approving it for publication was Bidyadhar Subudhi . these grippers are limited to transporting simple forms of objects, which is a pick-and-place.

A. ANTHROPOMORPHIC ROBOT HAND
Recently, the anthropomorphic type of robot hands that can grasp and interact with various objects have been studied [5], [10]. The anthropomorphic type robot hand is a form that mimics a human hand, and it is a multi-finger type with 4-fingers or more (shown in figure 2). It is more capable of broader applications than the simple gripper type end-effector. In the last five years, most studies about the anthropomorphic robot hand have been designed with an under-actuated mechanism.
Santina et al. [5] deal with the complexity-dexterity tradeoff by proposing a novel framework for the design of tendon driven under-actuated hands. According to the authors, the SoftHand 2 can manipulate objects of different shapes with just two DoA (Degrees of Actuator) and requires only a very simple control strategy. However, there is no feedback system for the external environment and it cannot force control. You et al. [7] proposed the anthropomorphic robot FIGURE 1. Fingered end-effectors: (a) 2-finger type, (b) 3-finger type [3], [4].
hand with a backdrivable mechanism, an ADP (active distalproximal) joint, and IMC (intermetacarpal) joints. This robot hand is developed to have a closer dexterity to the precision grip of the human hand without any complex control algorithm. For the evaluated the developed robot hand, they are using their own gripping strategy: the coordinate center of the workspace intersection volume of the robot fingers is used as the gripping point. Cheng et al. [8] proposed a high-level integrated under-actuated anthropomorphic finger with three joints and two DoF (Degree of Freedom). Moreover, this finger led to the design of a novel coupled-adaptive mechanism, and it has a multi-channel tactile sensor, angle sensor for the force and position feedback. Yoon and Choi [9] presented an under-actuated finger mechanism for implementing three DoFs motion with only one linear actuator and two springs. The aim of this research is to design a robotic finger able to perform not only natural motion but also self-adaptive grasping. Kim et al. [11] proposed the FLLEX Finger, a 3-DoF (Degree of Freedom) finger mechanism that is cable-driven with unique VEC pulleys, which allow high fingertip force and accurate kinematic modeling. As all the moving parts are submerged in lubrication fluid with a latex skin, the finger mechanism has high efficiency and control performance. Mańkowski et al. [12] developed the PUT-Hand, the five-finger anthropomorphic gripper intended for elastic object manipulation. PUT-Hand is a hybrid design, taking advantage of both fully actuated and under-actuated designs. This robot hand is equipped with tri-axial force sensors mounted on the fingertips of fully actuated fingers (index, middle, and thumb).

B. VARIABLE GRASPING STIFFNESS OF THE ROBOT HAND
The studies introduced in this part about the variable grasping stiffness of robot hands (gripper) are a method of manually controlling the grasping stiffness by transmitting the information of the object (mass, size, material, etc.) to the robot hand. Alternatively, the body of the robot hand (gripper) is composed of soft materials to minimize damage to the grasping object and control the grasping stiffness [13]- [18]. These established methods show that if the robot hand (gripper) controls the grasping stiffness, various objects can be grasped without damage. However, there is a limitation of manually controlling grasping stiffness.
Nagase et al. [13] developed the pneumatic robot hand with variable-stiffness fingers that can change their softness and friction. This robot hand consists of silicone rubber, fiber reinforcement, and the joint part. The softness and friction coefficient of the proposed finger can be changed by adjusting the input air pressure to the variable-stiffness finger devices. Abeach et al. [14] designed and tested a variable stiffness, three-fingered soft gripper. The gripper uses pneumatic muscles that are soft and inherently compliant. The stiffness of the gripper can be increased by raising the pressure in all the actuators that compose the pneumatic muscles, without the position of the fingers changing. Li et al. [16] present a novel structure-controlled variable stiffness robotic gripper that enables adaptive gripping of soft and rigid objects with a wide range of compliance. However, before grasp execution, the desired grasping force and the object size should be defined or pre-measured since the gripper is open loop controlled without using any force sensors at the gripper tips. Mahboubi et al. [17] introduced a mechanism that provides a driving force for tendon-driven hands to control the position and stiffness of the fingers with two servo motors. However, the grasping stiffness is manually controlled by the desired spring compression. Sun et al. [18] designed and fabricated a soft gripper with variable stiffness contributed by a pangolin inspired structure and an enhanced pneumatic actuator, and the grasping stiffness is controlled by air pressure.
The aim of this study is to develop an anthropomorphic robot hand that has variable grasping stiffness (not manually controlled) to unknown objects. This robot finger integrates the force sensor, a piezo-resistor style sensor. Our conclusion is that the proposed robot hand can detect the object's elasticity when grasping an object and react to adjust the grasping stiffness. To do this, we applied the variable impedance control using a parameter update (the detailed description written in Section III). We also demonstrate the robot hand's ability to adjust the grasping stiffness by detecting elasticity of the object using sensors of the robot finger, and the basic ability of the robot hand (grasping force, fingertip force, and flexion/extension velocity etc.).
The paper is organized as follows. We explain the mechanical/electrical hardware of the developed robot hand and analyze the kinematics to understand the correlation of the workspace with respect to the joint space in Section II. Section III describes the controller that actuates the robot hand. The impedance controller is constructed using feedback from the fingertip force sensor and the series elastic actuator module sensor for the grasping stiffness. The proposed robot hand performance is tested through several experiments in Section IV. The conclusion is provided in section V.

II. DESIGN OF THE ROBOT HAND HARDWARE
Based on the kinematics configuration of the human hand [19]- [21], this section introduces the anthropomorphic robot hand design. The fingers, except the thumb, were composed of four links and three joints [22]- [24]. Based on the kinematic configuration, the robot finger is designed to be modularized. The robot finger modules are constructed with a thumb, index, middle, and ring finger to complete the anthropomorphic type robot hand.  The purpose of this paper is to implement three DoFs as one actuator based on an under-actuated mechanism. The robot finger is determined based on the linkage mechanism with less transfer force loss of the actuator than those that are tendon-driven. Two four-bar linkages are connected in series, as shown in figure 4, so that the robot finger moves according to the actuator movement. The four-bar is the most straightforward movable closed-chain linkage. It consists of four links connected in a loop by four joints [25]. Link A corresponds to the MP in the human finger, and Link B corresponds to the PP. The actuator uses a PQ12-P linear actuator (Autonix Co., Canada), and the actuator shaft moves forward/backward according to the control signal. This actuator has a potentiometer for feedback of the actuator shaft position. The robot finger has sensors which are force sensors and a SEA (Series Elastic Actuator). As shown in figure 4 (a), the DP body has a force sensor to measure the fingertip force. The force sensor is a FSG15N1A (Honeywell Co., USA), and is detected by the piezo-resistor style. The SEA (Series Elastic Actuator) module developed in the actuator shaft (motor output) is connected. The SEA can calculate external force using Hooke's law by measuring the length of the spring. To this end, the linear potentiometer is fixed to the SEA body to measure the length of the spring. The specifications of the finger module and sensors are shown in table 1.

B. KINEMATICS OF THE ROBOT FINGER
The robot finger changes the position and orientation of each link at the joint. Kinematic analysis is required to predict the position and orientation of the link with the movement of the joint. The robot finger module analyzes kinematics based on vector analysis, as shown in figure 5. In this kinematics analysis, the variable vectors are q, r n , and p n , and the constant vectors are a n and b n . The vector q is an input element of the robot finger, which expresses the movement of the actuator; and the vector p n changes orientation, according to q, but the size does not change. Similarly, among the included angles of two different vectors, the variable angles are θ n and α n , and the constant angle is δ n . The constant vectors a n and b n , and angle δ n are fixed values determined in the design, and r n is an adjusting vector for vector analysis. body fixed to the metacarpals and vectors a 1 and p 1 are an actuator dimension offset. The vector p 2 is a part of the SEA module, and its size changes by an external force. However, since the kinematics analysis in this chapter proceeds in the no-load state, the size of vector p 2 is fixed.
The variation of MCP, PIP, and the DIP joint by q is calculated as follows; θ m , θ p , and θ d respectively represent the angle of the MCP, PIP, and DIP joints.
The robot finger module RoM (Range of Motion) simulation result is shown in figure 6, based on the kinematics analysis in (1) -(4).

C. ROBOT HAND HARDWARE
The designed robot hand is shown in figure 7. The main board contains a microprocessor, a low-pass filter circuit, a Bluetooth module, and a battery. The Hand palm board has the motor driver modules, the actuator connectors, and variable sensor connectors. The fingertip boards have amplifiers for the force sensors and force sensor's connectors. The detailed specifications of the robot hand are shown in table 2. The size of the robot hand is similar to an adult men's (age 20-60) average hand size [26] (193.04 mm). Additionally, the detailed experiment of grasping force in shown in Section IV.

III. VARIABLE GRASPING STIFFNESS CONTROL A. CONTROL ARCHITECTURE
The overall control architecture of the robot hand is shown in figure 8. The MCU (micro controller unit) is A/D (analog to digital) converting various sensor signals (actuator encoder, force sensor, SEA module sensor) to control the robot hand. The sensor signal is used as a feedback factor, and the   designed controller operates the actuator. Further, the MCU communicates with a PC based on Bluetooth wireless communication. The total control cycle is 500 Hz, and the main clock of the MCU is set to 168 MHz.

B. VARIABLE IMPEDANCE CONTROL
Impedance control focuses on controlling the correlation between external force and motion, rather than handling position control and force control as separate problems. Applying impedance control to the robot fingers achieves the same effect as the fingertip points connected to the virtual compliance frame origin with a mass-spring-damper [27]. When the robot hand grasps the object, it should be able to determine the elasticity of the object according to the contact force. Previous studies quantified the flexibility of objects based 99470 VOLUME 9, 2021   on the Shore hardness scale [28]- [32]. The Shore hardness scale is written as ''50 Sh SRIS,'' which means the higher the number, the harder the object and the lower the number,   the softer the object. When the output power of the robot finger is the same, the external force detected at the fingertips is changed by the hardness of the object. Therefore, the relationship between the Shore hardness and the external VOLUME 9, 2021  force (f) detected in the robot finger should be defined, and the parameter of desired impedance should be adjusted based on the Shore hardness. In this paper, the parameter update block, which can adjust the desired impedance parameter, is added to the general impedance controller shown in figure 9.
The parameters of the desired impedance are the damping ratio (ζ ) and natural frequency (ω n ). There are several studies that apply variable impedance control by manipulating the parameters of the desired impedance [33]- [39]. In some cases, the variable impedance control is implemented by controlling the virtual damping ratio, [33], [34], and the parameter using the damping ratio is handled with a fuzzy algorithm and adjusted [35], [36]. There are cases where the pattern of the damping ratio is defined, and the experimental results are discussed for each situation [37]. To control the stiffness parameter, some cases are implemented by reflecting the damping ratio [38]. There are also cases where the variable admittance control is implemented by changing the damping parameter of the controller based on the rate of change of the force [39]. Therefore, in this paper, the parameter update block is implemented with a focus on the damping ratio. The detailed flow chart of the parameter update block is shown in figure 10. When the robot hand grasps the object, the peak value is detected in the measured force. The Shore hardness is estimated based on the peak force value, and the damping ratio is calculated from the estimated Shore hardness. In the Laplace domain, the position error e x (s) modified by the impedance compensator, and the position compensation x f (s) are defined as (5) -(6), where x (s) is the current  First, we define the relationship between the Shore hardness and the damping ratio. The precondition for expression of a relation is when an object is grasped, slip does not occur, and the object's weight and size are not considered. For this purpose, the range of stable grasping is searched   using a trial and error method based on the selected object, as shown in figure 11. As a result, if ζ is smaller than 0.45, VOLUME 9, 2021 it is impossible to grasp the object stably due to excessive vibration, and if ζ is larger than 1.25, the robot finger's has insufficient output, making it impossible to grasp stably. Therefore, the search range is set up as 0.45 ≤ ζ ≤ 1.25. The grasping experiment is carried out for each object within the set range. The data obtained from the experiments are shown in table 3. The range of ζ for each object is the range of fast settling time after analyzing the response characteristics of the robot finger position. The ζ d is set to a median value in the range of the estimated ζ . Additionally, the peak force means the maximum force at the moment when each object is grasped.
The correlation between the Shore hardness and ζ d is defined as (7), where h s is a Shore hardness and α i is a coefficient of each term. The correlation of h s and ζ d of (7) is a quadratic curve fitting based on the least-squares regression (R 2 = 0.998 of (7)). When the robot hand grasps the object, it should be able to determine the Shore hardness of the object with the value of the measured force sensor. Thus, when grasping objects 1 -5, the correlation between the detected peak force and the Shore hardness is defined as (8). The correlation of h s and f p of (8) is an exponential curve fitting based on the least-squares regression (R 2 = 0.997 of (8)), where f p is a peak force and β i is a coefficient of each term (where, 0 ≤ h s ≤ 100). The final correlations of f p , h S , and ζ d are shown in figure 12. After assuming the fingertip contact point as an impedance model to grasp an object, it is used after classifying the tendency through repeated experiments. Therefore, rather than directly estimating the impedance, a method of estimating the tendency and using it for the control parameter is proposed. In this chapter, the experiments conducted to define the correlation between f p − h S − ζ d were all obtained through more than twenty repeated experiments, and (7) -(8) were determined based on the average values.

C. EVALUATION OF VARIABLE IMPEDANCE CONTROL
The variable impedance controller, in which the damping ratio is controlled due to the parameter update block, is verified. The experiment is based on six objects, and each character is shown in table 4. The durometer measures the Shore hardness in table 4, ζ d is estimated based on (7), and the ζ is experiment data from the proposed the robot hand system. The results of the experiment are shown in figure 13. The red line is the data obtained from the experiment, and the blue dashed line represents the desired data of objects used in the experiment. As a result, there is an error between ζ d and ζ (in figure 13 (b) -(e). The maximum error is 0.006, but the effect on the controller is minimal, so the goal of this paper can be implemented.

IV. GRASPING EVALUATION EXPERIMENTS
Before the grasping evaluation experiments, it is necessary to quantify the performance of the robot hand. Mechanical specifications (finger/hand size, spring parameter etc.,  as indicated in tables 1 -2) do not require an experiment for quantification. However, in the case of fingertip force, grasping force, and finger speed, experiments for quantification are needed.

A. EXPERIMENT FOR ROBOT HAND SPECIFICATIONS
The fingertip force and finger speed of the robot finger module are measured in an environment shown in figure 14. The fingertip force is measured by using the F/T (force/torque) sensor (HEX-70-XE-200N, Optoforce Co., Denmark), as shown in figure 14 (a). At his time, the movement of the SEA module is fixed to the spring stopper; the robot finger is not compressed due to the external force.
The jig is developed for measuring finger speed, as shown in figure 14 (b).
The PIP and DIP joints are dependent on the MCP joints, thus measuring the angular velocity of the MCP joints. The MCP joint angle is measured from the magnetic encoder (EzEncoder, i2A Systems Co., South Korea). The measured angle is differentiated according to time to calculate the angular velocity. The results of each experiment are shown in figure 15. The maximum average force of the fingertip is 5.3 N, and the average finger speed is 52.44 • /s.
To measure the grasping force of the robot hand based on the robot finger module, we made the cylinder type jig shown in figure 16. This jig has an FSR sensor built in to measure the grasping force of the robot hand. The measurement results are shown in figure 17, and the maximum average force is 35.7 N.

B. EXPERIMENT FOR ROBOT HAND GRASPING EVALUATION
The grasping method of objects used in the experiment is selected based on Cutkosky's grasping taxonomy [2]. Therefore, power grasp (prehensile -prismatic -circular) and precision grasp (circular -prismatic) should be implemented as an  object used in everyday life to verify the performance of the developed robot hand (in figure 17). The grasping method is changed by control commands from the PC to the MCU using wireless communication. To quantify, the hardness of the object used in the experiment should be measured; therefore, the hardness of each object is measured and classified. The hardness is a measure of the resistance to localized plastic deformation induced by either mechanical indentation or abrasion. To measure hardness we used a Shore durometer (Teclock Co., Japan).
The grasping evaluation was examined by using 21 objects of various size, weight, and hardness. The classification and the characteristics of objects used in experiments are shown in figure 18 and table 5. When the robot hand grasps the object, if it is in the food group, it is easy to identify damage to the object with the naked eye. Therefore, the No. 16 -21 objects are selected as the food group. The experiments perform pick-and-place tasks with the robot hand mounted on the manipulator (UR3, Universal Robot Co., Denmark), as shown in figure 20 (on page 9). Figure 19 (on page 10) shows selected video-captured images of this task for eight different objects, and figure 21 (on page 11) shows the results of the evaluation experiment about damping ratio and hardness value according to time of the selected eight objects. The experimental results show that the proposed robot hand grasps each object without damage and completes the given task, and when the robot hand grasps the object, the damping ratio and the shore hardness value change according to time. This means that the parameter update block for the impedance controller operates without any abnormality based on the detection of the object's flexibility by a force sensor. However, small experimental objects, such as the USB stick, AA battery, coin, tangerine piece, and credit card, could not be grasped. In particular, the object was flat on the surface of the table, so the robot hand could not get a grip. On the other hand, when a person delivers an object to a robot hand, such as the hand-over task in figure 22, it is easy to grasp. This is possible because the task environment is adjusted so that a person can directly grasp the robot hand. The developed robot hands have these limitations.

V. CONCLUSION
In this article, we developed an anthropomorphic robot hand using a series elastic actuator module, which has variable grasping stiffness to handle unknown objects without damage. To do this, first we studied the skeleton structure of human fingers to design an anthropomorphic robot finger. Based on the kinematic configuration, the robot fingers, except the thumb, were composed of four links and three joints [19]- [24]. Second, we explain the mechanical/electrical hardware of the developed robot hand and analyze the kinematics to understand the correlation of the workspace with respect to the joint space. The purpose of this paper is to implement three DoFs as one actuator based on an under-actuated mechanism. The robot finger is determined based on the linkage mechanism. The SEA (Series Elastic Actuator) module developed in the actuator shaft is connected. Also, for detecting the external force of the fingertips, we used a force sensor. The robot finger module analyzes kinematics based on vector analysis. And the variation of the MCP, PIP, and the DIP joints by q has been calculated. The robot hand consists of four fingers (index, middle, ring, and thumb). It is sized similar to an adult male hand. Third, we describe the controller that actuates the robot hand. The total control cycle is 500 Hz, and the main clock of the MCU is set to 168 MHz. The parameter update block, which can adjust the parameters of the desired impedance, is added to the general impedance controller. The parameter update block adjusts the parameters of the desired impedance based on the Shore hardness scale [28]- [32]. The parameters of the desired impedance are the damping ratio and the natural frequency. In this paper, the parameter update block is implemented with a focus on the damping ratio by referring to studies about variable impedance control [33]- [39]. Therefore, the correlation between the detected peak fingertip force, Shore hardness, and desired damping ratio values was defined. Finally, we verified the experiment for the specifications of the robot hand and the grasping capability by performing various experiments.
For further works, the grasping experiment conducted in this study is not an optimal grasp test for the target object because it is conducted without a separate recognition algorithm, and the three fingers of the robot hand, except the thumb, can only move via flexion/extension. For more diverse movements, it is necessary to repair the adduction/abduction motion. Therefore, further studies on the optimal grasping of objects that robot hands are trying to grasp should be conducted, and the DoF of robot hands should be increased for more diverse movements. Based on this, further research needs to be done to enable in-hand manipulation. He was a Postdoctoral Fellow with the University of Illinois at Urbana-Champaign, in 2003. He founded the HRI Laboratory, Kyung Hee University, which performs research in human-robot interaction, service robotics, cooperative robotics, and multi-robot systems. Prior to his position at Kyung Hee University, he was in industrial and commercial hardware development as a Senior Engineer at Samsung Electronics for three years. In that experience, he developed and led numerous mobile phone projects. He has been a Professor with the Department of Electrical Engineering, Kyung Hee University, South Korea, since 2007. His current research interest includes multi-agent robot systems.
Dr. Kim serves on the Board on International Robot-Soccer Committee, Intelligent Robot Standards Forum, and Institute of Control, Robotics and Systems. VOLUME 9, 2021