1. Introduction
The robot gripper is a useful and important component of an automated system. It is often used to pick up and place a given object on an assembly line in production. It is also used for complex tasks such as assembly of microelectronic components, surgery, etc., or in areas that have hazardous conditions such as high temperature or toxic chemicals [
1]. There are many actuation principles used in grippers with mechanical, pneumatic, hydraulic, electric, or piezoelectric actuators, etc. Along with the development of technology, the grippers have been brought to a new level. The grippers not only grip, pick up, and place objects to a new position but also are equipped with sensing capabilities to adapt to changing environments [
2].
In automated production, one of the important requirements of grippers is the ability to safely grasp and hold fragile objects of varying stiffness and shapes. Using flexible grippers is one of the solutions. In [
3], embedded sensors are used to ensure the safe and optimal behavior of the gripper. The authors establish soft computing methods including extreme learning machines and support vector regression to achieve the prediction of optimal input displacement of the gripper. The authors of [
4] deal with a multiobjective optimization problem using a genetic algorithm, while [
5] establishes a direct force control for a three-finger adaptive robot gripper by using a proportional-integral-derivative (PID) control to grasp objects without damaging them. Suebsomran [
6] proposes a new design to control a robot gripper based on the grasping force method. The force controller is designed by using a PID control algorithm with different control gains and objects tuning by experiment methods. A high-speed multifinger reconfigurable gripper is presented in [
7]. The gripper can grasp parts with varying geometrical and physical properties at high speed and accelerations. In [
8], the authors use a force-sensitive resistor (FSR) to grasp novel objects adaptively with minimal gripping force. A laser-based optical slip sensor is embedded in its fingers to prevent the object from sliding down. The authors of [
9] deal with a microgripper driven by piezoelectric actuators. The authors propose an adaptive online estimation scheme to calculate uncertain parameters in the dynamics model and the Kalman filter to predict the system output. Although there is a lot of research in literature, novel control applications are being studied to enhance gripper performance. This paper proposes an intelligent control approach for a robot gripper with the main objective of controlling the optimal gripping force in real time for unknown objects.
The impedance control is used to keep the gripping force at the desired value. Impedance control is an indirect force control method and very popular in interaction control because of its robustness and feasibility [
10,
11,
12,
13,
14]. However, in the impedance control method, the interaction force is changed from environment to environment and even within the same environment over time. Therefore, it is hard to determine the desired parameters of the impedance controller. In [
15], the authors propose a new simple stable force tracking impedance control scheme. The main idea is to minimize the force error directly by using a simple adaptive gain when tracking an unknown environment. In [
16], a novel adaptive impedance control is proposed for the robotic manipulator in assisting the operator to perform the human–robot cooperative task. It can optimize the impedance parameters with little information about the model. The authors of [
17] use the equilibrium point control theory and reinforcement learning to determine the impedance parameters for contact tasks. In [
18], The gradient-following and betterment schemes are employed to obtain the desired impedance model, subject to unknown environments. In [
19,
20,
21,
22], the combination of fuzzy logic and traditional impedance control is proposed to enhance the control performance.
The fuzzy logic [
23] can deal with nonlinear and uncertain systems, so it can be used to estimate the optimal impedance parameters in real time. However, its effectiveness depends on the rule base, which is built on the initial sample dataset. This paper proposes a combination of iterative learning control (ILC), fuzzy logic, and impedance control. The ILC based on the gradient descent algorithm [
24,
25] is used to determine the impedance parameters in unknown environments. However, the ILC process takes time for the impedance parameter to converge to the desired optimal value. Therefore, it is not conducive to perform in real time. Instead, it is performed with various sample objects to synthesize a sample dataset of optimal impedance parameters. This dataset is then used to design the rule base of the fuzzy impedance controller, which will run in real time to estimate the optimal parameters of impedance control under each given condition.
Another important requirement of grippers is to keep an unknown object from sliding down after gripping and picking it up. In [
26], the authors develop a microlaser Doppler velocimeter as a sensor to detect whether a grasped object is slipping or not. In [
27,
28], a biomimetic tactile sensor is used to detect and classify slip events. These methods require complicated installation at the contact between the gripper’s finger and the object. In this paper, a six-axis force/torque sensor (FTS) mounted on the gripper will be used to design the gripping force estimator, which will calculate the appropriate gripping force in real time to keep the unknown object from sliding down instead of trying to detect slippage. The FTS is simple to mount and avoids direct contact with the object. It also proves effective when it is possible to quickly and accurately estimate the optimal gripping force when picking objects up.
The main contribution of this paper is the proposal of an optimal fuzzy impedance controller, which can operate in real time to safely grasp and hold fragile and unknown objects of varying stiffness and shapes. The optimal fuzzy impedance controller is the combining schema of the impedance control, fuzzy logic control, and ILC. Many studies mention the combination of impedance control and fuzzy logic but do not specify the process of building the sample data for designing the rule base, which plays a very important role in determining the effectiveness of the fuzzy controller. In this study, the ILC process is employed to optimize the sample dataset for designing the rule base to enhance the effectiveness of the fuzzy impedance controller. Besides, the design of the gripping force estimator based on an FTS is a simple but effective application proposal in keeping an unknown object from sliding down when picking it up. Compared with other methods, such as PID control, the proposed method has advantages in that the control parameters are automatically estimated in real time and the force control has higher accuracy and stability. Its effectiveness has been verified by conducting the simulation, experiment, and comparison.
The following content of the paper is organized as follows:
Section 2 describes the control schema and system description.
Section 3 presents the impedance iterative learning control.
Section 4 describes the fuzzy impedance controller.
Section 5 presents the simulations, experiments, and comparisons.
Section 6 discusses the results.
Section 7 is the conclusion.
2. Control Schema and System Description
Figure 1 illustrates the model of the two-finger gripper used to apply the optimal fuzzy impedance controller. The FSR is fitted below the finger pads to provide gripping force value. The gripper is attached to the FTS fixed on the end effector of the Hexa robot. The FTS measures the weight of the object, which is gripped and picked up.
Figure 2 is the architecture of the optimal fuzzy impedance controller, including three blocks: position control, force calculation, and optimal fuzzy impedance control.
The position control block, using a common PID controller, is responsible for controlling the position of the fingers to the desired position . The value is determined by the initial reference position and the position compensation . For picking up objects of unknown shape and size, the value is set relative to the gripper’s fully closed position.
The force calculation block includes FSR and FTS. The gripping force
is measured by the FSR. The object weight
is measured by the FTS.
is the initial gripping force defined by the user. At the beginning of the gripping process, the desired gripping force
is assigned by the value of
. When the gripper starts to pick the object up, based on the value
, it will calculate an appropriate value
to prevent the object from sliding down. The calculation
is presented in
Section 3.4.
The optimal fuzzy impedance control block has three sub-blocks: impedance controller, ILC, and fuzzy controller. The impedance controller calculates the position compensation value for the position control block based on the force error , the initial reference position of fingers , and the current position of fingers . It is the key control, which ensures the gripping force is always kept at a sufficient force. The ILC is derived from the gradient descent algorithm to find optimal parameters and of the impedance control in unknown environments. This is the initial learning process. For each kind of object (with various hardness) and various closing speed, the ILC is performed to find an optimal data of impedance parameters. By changing the object material, closing speed, and repeating the ILC, an optimal dataset of impedance control is built for further creating a rule base for the fuzzy controller. Based on this rule base, the fuzzy controller calculates the best impedance parameters simultaneously when the gripper fingers touch on the object surface. If the fuzzy controller cannot match any rule in the rule base, the ILC is recalled to calculate new appropriate parameters of the impedance control. If these parameters make the control reach the desired state, they will be analyzed to create new rules and added to the rule base.
3. Impedance Iterative Learning Control
This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation as well as the experimental conclusions that can be drawn.
3.1. The Impedance Control
This section presents the basic structure of the impedance controller, which keeps the gripping force at the desired value. The model of impedance control can be expressed as:
where
,
, and
represent inertia, damping, and stiffness parameters, respectively.
and
are the reference and current positions of the fingers of the gripper, respectively.
is the force error, which is based on the desired force
and the current gripping force
.
The dynamic behavior of the model is determined by the damping ratio
, which is expressed as:
For gripping the object with a sufficient force and without oscillation, the damping ratio must be greater than or equal to one (critical damped or overdamped). In practice, it is adjusted to be greater than one (overdamped state) to both eliminate oscillation and ensure the desired gripping force.
3.2. The Iterative Learning Control
The ILC is proposed to optimize the impedance parameters for various objects and closing speeds. The inertia parameter is fixed at an apparent value selected by the experiment based on the mass of the gripper fingers. Because the damping ratio is fixed, only the damping parameter is updated during the ILC process. The stiffness parameter is calculated by Equation (2).
The gradient descent ILC algorithm [
24] is applied to derive the learning law. The general form of this algorithm is expressed as:
where
is the iteration number.
is the input applied to the ILC process.
is the learning gain.
is the transfer function of the nominal model.
is the output error. The product
determines the direction of the update vector.
The convergence of Equation (3) is guaranteed if [
24,
25]:
The gripping process tracks the gripping force, so the output error is determined as:
The input
of the ILC process in Equation (3) is the damping parameter
. The transfer function
is calculated based on the gradient scheme to ensure a gradual change of the gripping force by updating
. It is derived as:
From Equations (3), (5), and (6), the learning law is formed as:
From Equations (4) and (6), the convergence condition of the ILC is determined as:
In each iteration of the ILC process, the learning gain is adjusted to satisfy the condition in Equation (8).
The ILC process is stopped if the following conditions are satisfied:
where
is the iteration number.
is the maximum overshoot of the gripping force.
is the final force error.
is the desired value.
3.3. The Implementation of ILC
The ILC process is described as follow:
STEP 1: Start the process
Starting with a certain object, the desired closing speed , and a desired gripping force .
STEP 2: Initialization
Loading the initial values of , , , , and .
STEP 3: Start a learning loop
Fully opening the fingers of the gripper. Clearing the temporary storage. Starting the gripping timer. The gripper gradually closes the fingers with the desired speed until the fingers touch on the object’s surface. The system starts to measure and track the value of .
STEP 4: Iterative learning
In each sample time, the system measures the contact force and calculates the values of and . The learning gain is determined by the condition in Equation (8). The new value of is calculated by Equation (7). The parameter is calculated by Equation (2). The new values of , , , and are added to the temporary storage as a record and loaded to the system for the next sample time. Repeating Step 4 with each sample time until the gripping force is stable or the gripping timer reaches a limit value.
STEP 5: End the learning loop
Checking the stopping condition in Equation (9). If it is satisfied, move to Step 6, otherwise, start a new loop from Step 3.
STEP 6: Finish the process
Recording the optimal values of ILC: each record in the temporary storage combines with the values and in Step 4 will create a new data record in the dataset.
3.4. The Gripping Force Estimator
Figure 3 shows the force diagram of griping and picking up the object.
is the weight of the object that is calculated from the parameters of FTS.
is the gripping force of fingers.
is the friction force.
, where
is the friction coefficient between the finger pad and the object surface. To prevent the object sliding down, the gripping force must be satisfied:
In the implementation, the gripping force is set as:
where
is the antisliding coefficient.
The friction force is set approximately by experiment based on the materials of the finger pad and object surface. The antisliding coefficient is set according to the real model. In this study, is set to 1.4 for the best performance.
4. Fuzzy Impedance Controller
Through the experiment, the ILC works very well. However, the best impedance parameters found by ILC are only fit to a specific environmental condition, including object properties and closing speed. If the environment is changed, the ILC needs to be performed again. Therefore, the fuzzy impedance controller is proposed to calculate the best impedance parameters simultaneously based on the knowledge from training without repeating the ILC process.
4.1. The Data Collection for Designing Fuzzy Impedance Controller
The ILC process in
Section 3.3 provides the data record of the best impedance parameters for a specific environment. By changing either the object hardness or desired closing speed
and repeating this process many times, an optimal dataset is built for creating the rule base of the fuzzy impedance controller. It is necessary to note that the important parameters in the data record of the ILC learning process are the gripping force error
, the closing speed
, the optimal damping
, the optimal stiffness
, the maximum overshoot
, and the final force error
.
4.2. Fuzzy Logic Design
The main objective of the fuzzy impedance controller is to estimate the impedance parameter . Based on the learning law of ILC in Equation (7), the fuzzy system is designed consisting of two inputs: the gripping force error and the closing speed . The output is the damping . The parameter is calculated by Equation (2) after the damping is estimated.
Figure 4 shows the triangular membership functions of inputs and output. The number of fuzzy regions of inputs
,
, and output
is
,
,
, respectively. The inputs
and
are recorded at the time when the fingers just touched the object for the first time, so these parameters have negative values and magnitude depending on the closing speed and object hardness. The output
is always positive. Based on the dataset collected from the data collection as presented in
Section 4.1, the maximum magnitudes of the inputs and output are determined to set the values of
,
, and
. The number of fuzzy regions
,
, and
are experimentally adjusted so that the fuzzy controller achieves high accuracy.
The fuzzy impedance controller employs Mamdani If-Then rules as the following form:
The rule: If is and is then is , where ; ;
The dataset will be preprocessed to filter noise based on the maximum overshoot and the final force error . Its final data records will be calculated to create the rule base.