**6. Robotic gripper modeling**

94 Fuzzy Inference System – Theory and Applications

It may not be possible to apply all the guidelines to any one design. Sometimes, one guideline may suggest one design direction while another may suggest the opposite. Each particular situation must be examined and a decision must be made to favor the more

2. Grasp objects securely: This allows the robot to run at higher speeds thereby reducing

6. Minimize finger length: Obviously, the longer the fingers of the gripper the more they

7. Design for proper gripper-object interaction: If, however, a flat surface is being used, then a high friction interface is desired since the part would not be aligned anyway and

The objects may vary in size and shape. Thus the gripper should be able to handle objects of different shapes and sizes in a particular range. Gripper should be compact so that it does not interfere with other equipment. The use of conical fingers "three fingers or more" will help holding the parts securely. But if we have an object larger than these conical fingers, the object could not be gripped properly. Parallel moving fingers are a good solution in this case. This parallel movement also helps in gripping objects internally. Since the force is acting at a point or line in conical form of gripping it may lead to wear and tear of both the object and the finger. But in the parallel finger arrangement, the force will be distributed over an area. The two-fingers grasp may be

The developed gripper device was configured with a two parallel finger design for its wide applications in spite of its precise control need. One finger is fixed and the other is movable to ease the control and minimize the cost as shown in figure 4. The fingers are flat and rectangular in shape. The housing of the gripper and fingers were made of aluminum sheet for light weight consideration with proper thickness to ease the machining and holes puncture through edges. This gives simple assembly and ease in maintenance. The movable finger is driven on a lead screw and guided by a linear bearing system with the advantage

To control the gripping of the object, we need to measure both the force applied to the object and the object slip. A standard commercial force sensor resistor FSR (Flexiforce A201 working in the range of 0-1 lb (4.4N)) is used to measure the applied force. Also Phidget vibrator sensor is adapted as slip sensor to give information about object slip rate in m/sec. These two sensors are tactile sensors. The actuator used to drive the movable finger is a

relevant guidelines (Monkman et al,2007). The design guidelines may be as follows: - 1. Minimize the gripper weight: This allows the robot to accelerate more quickly.

3. Grip multiple objects with a single gripper: This helps to avoid tool changes. 4. Fully encompass the object with the gripper: This is to help hold the part securely. 5. Do not deform the object during grasping: Some objects are easily deformed and care

should be taken when grasping these objects.

are going to deflect when grasping an object.

**5.1.2 Two fingers gripper selection** 

**5.1.3 Gripper configuration** 

the higher friction increases the security of the grasp.

considered the simplest efficient grasping configuration.

of self-locking capability, low cost and ease of manufacture.

**5.1.1 Gripper design guidelines** 

the cycle time.

To build the proposed controller, we need to get information about the system characteristics for use in simulation and experimental work. Hence, input/output variables of the system are measured and processed. The input variable to the system is the speed control command to the servo motor drive expressed as reference voltage Vref . The applied force on the object is the output variable Fapp. The deformable compliant rubber material covering the contact area of the fingers, as shown in figure 4, is important to allow a wide range of force control for solid objects as well as decreasing the pressure on the object and increasing the friction. Hence, we need to model the variation of the applied force Fapp by the gripper finger with time at different reference voltage control commands Vref .

Fig. 4. Gripper configuration.

Experimentally, and due to the mechanism constraint according to the gripper design, the applied force by the gripper fingers Fapp on the objects could not decrease if the reference voltage control command Vref is decreased. To verify the proposed controller, a model was built using MATLAB software package considering the mechanical constraints, which in turn lead to the accumulation of the applied force when Vref is changed. For practical control, a maximum limit was set to the applied force Fmax.app , figures 5 & 6. From this simulation model, the set of training data, checking data and testing data to be used for ANFIS model training were prepared.

Control of Efficient Intelligent Robotic Gripper Using Fuzzy Inference System 97

The experiment was set up as shown in figure 8. Different masses were used for calibration considering the maximum force that can be applied to the sensor according to its data sheet. The whole sensitive area should be subjected to the applied force. Using the nonlinear least squares fitter we can fit a function to our recorded measurements as shown in figure.9. From the force sensor data sheet, the sensitive area is 0.7136 cm2, whereas the contact area between the object and any finger is 6.25 cm2 "the rubber material has a contact surface

**6.1 Force sensor calibration and modeling** 

Fig. 8. Experimental test for force sensor calibration

Fig. 9. Allometric function curve fitting.

Fig. 5. Gripper prototype.

Fig. 6. Gripper simulation using MATLAB considering the maximum applied force.

Fig. 7. Gripper simulation results considering the maximum applied force.

#### **6.1 Force sensor calibration and modeling**

96 Fuzzy Inference System – Theory and Applications

Fig. 6. Gripper simulation using MATLAB considering the maximum applied force.

Time in seconds

Fig. 7. Gripper simulation results considering the maximum applied force.

Fig. 5. Gripper prototype.

The experiment was set up as shown in figure 8. Different masses were used for calibration considering the maximum force that can be applied to the sensor according to its data sheet. The whole sensitive area should be subjected to the applied force. Using the nonlinear least squares fitter we can fit a function to our recorded measurements as shown in figure.9. From the force sensor data sheet, the sensitive area is 0.7136 cm2, whereas the contact area between the object and any finger is 6.25 cm2 "the rubber material has a contact surface

Fig. 8. Experimental test for force sensor calibration

Fig. 9. Allometric function curve fitting.

Control of Efficient Intelligent Robotic Gripper Using Fuzzy Inference System 99

**Data Points**

Fig. 13. Surface rules viewer for the developed FIS model using ANFIS.

It is known that the occurrence of slip for a solid object during grasping and lifting mainly depends on its mass, its coefficient of friction and also on the applied forces. If the applied force is not enough, acceleration is generated which leads to increased rate of slip and object dropping after certain time. This time depends on the applied force, the object mass and the coefficient of friction. Equation 3 determines the object acceleration as a function of

Fig. 12. Training data.

**6.3 Object modeling** 

dimensions 2.5cm x 2.5cm". Hence, there is a conversion factor, which converts the applied force by the finger on the object to the applied force on the sensor area as follows: -

$$F\_{app} = 8.76 \text{ } F\_{sens} \tag{15}$$

Using the proposed drive circuit shown in figure 10, we can deduce a formula that describes the relation between the analog output voltage from the force sensor and the applied force by the gripper finger as follows: -

$$V\_{out} = 5 \,\, ^\ast R\_f \,\, \, / \,\, \text{a} \,\, ^\ast \{ (F\_{app} / 8.76) \,\, ^\ast \text{b} \}\tag{16}$$

Where: a = 2807.18, b = -0.69019 and *Rf* = 65 Kohm

Fig. 10. Proposed drive circuit.

#### **6.2 ANFIS modeling for input/output gripper variables**

Adaptive Neuro-Fuzzy Inference Systems, ANFIS, are realized by an appropriate combination of neural and fuzzy systems and provide a valuable modeling approach of complex systems (Rezaeeian et al.,2008). The ANFIS structure is applied on our proposed robotic gripper, figure 11, based on the measured data which are simulated using MATLAB software package as shown in figure 6 and figure 7. We use 161 training data, 46 checking data, and 46 testing data. The training data are shown in figure 12. The surface rules viewer for the developed FIS model using ANFIS is shown in figure 13. Simulation results of the gripper using ANFIS modeling is shown in figure 14.

Fig. 11. Robotic gripper using ANFI.S

Fig. 12. Training data.

dimensions 2.5cm x 2.5cm". Hence, there is a conversion factor, which converts the applied

Using the proposed drive circuit shown in figure 10, we can deduce a formula that describes the relation between the analog output voltage from the force sensor and the

Adaptive Neuro-Fuzzy Inference Systems, ANFIS, are realized by an appropriate combination of neural and fuzzy systems and provide a valuable modeling approach of complex systems (Rezaeeian et al.,2008). The ANFIS structure is applied on our proposed robotic gripper, figure 11, based on the measured data which are simulated using MATLAB software package as shown in figure 6 and figure 7. We use 161 training data, 46 checking data, and 46 testing data. The training data are shown in figure 12. The surface rules viewer for the developed FIS model using ANFIS is shown in figure 13. Simulation results of the

*Fapp* = 8.76 *Fsens* (15)

*Vout* = 5 \* *Rf* / a \* (( *Fapp* /8.76) ^ b) (16)

force by the finger on the object to the applied force on the sensor area as follows: -

applied force by the gripper finger as follows: -

Fig. 10. Proposed drive circuit.

Where: a = 2807.18, b = -0.69019 and *Rf* = 65 Kohm

**6.2 ANFIS modeling for input/output gripper variables** 

gripper using ANFIS modeling is shown in figure 14.

Fig. 11. Robotic gripper using ANFI.S

Fig. 13. Surface rules viewer for the developed FIS model using ANFIS.

#### **6.3 Object modeling**

It is known that the occurrence of slip for a solid object during grasping and lifting mainly depends on its mass, its coefficient of friction and also on the applied forces. If the applied force is not enough, acceleration is generated which leads to increased rate of slip and object dropping after certain time. This time depends on the applied force, the object mass and the coefficient of friction. Equation 3 determines the object acceleration as a function of

Control of Efficient Intelligent Robotic Gripper Using Fuzzy Inference System 101

To measure the slip amount for an object subjected to grasping, lifting and handling, a piezoelectric vibration sensor was used. A piezoelectric transducer is displaced from the

Time in seconds

Fig. 17. Experimental tests for slip sensor calibration.

**6.4 Slip sensor calibration and modeling** 

Fig. 16. Object simulation results when Mass=100 gm and µ=0.5.

the normal applied forces by the gripper fingers and the coefficient of friction as shown in figure.14. Object simulation result is shown in figure.15, which indicates that the slippage is stopped after a period of time depending on the rate of force increase.

Fig. 14. Gripper simulation results using ANFIS modeling.

$$m \times a = m \times g - 2 \times \mu \times \mathcal{F}\_{app} \tag{17}$$

Where m is the object mass in kg, is the coefficient of friction, g is the earth gravity equal to 9.8 m/s2, and finally α is the object acceleration in m/s2

Fig. 15. Applied forces on the object.

the normal applied forces by the gripper fingers and the coefficient of friction as shown in figure.14. Object simulation result is shown in figure.15, which indicates that the slippage is

stopped after a period of time depending on the rate of force increase.

Fig. 14. Gripper simulation results using ANFIS modeling.

to 9.8 m/s2, and finally α is the object acceleration in m/s2

Where m is the object mass in kg,

Fig. 15. Applied forces on the object.

*ma mg F* 2

*app* (17)

is the coefficient of friction, g is the earth gravity equal

Fig. 16. Object simulation results when Mass=100 gm and µ=0.5.

#### **6.4 Slip sensor calibration and modeling**

To measure the slip amount for an object subjected to grasping, lifting and handling, a piezoelectric vibration sensor was used. A piezoelectric transducer is displaced from the

Fig. 17. Experimental tests for slip sensor calibration.

Control of Efficient Intelligent Robotic Gripper Using Fuzzy Inference System 103

the force needed to lift the object, but is a function of the object mass and its coefficient of friction. Figure 19 shows the block diagram of the first proposed controller scheme. Two

1. The first fuzzy controller is a reference voltage controller with two input variables, the

2. The second fuzzy controller is a gain controller for the output of the first controller with

integrated fuzzy controllers were built in this scheme as follows:

slip-rate and its derivative.

one input variable, the pushing force.

Fig. 19. Block diagram of the first scheme controller

Fig. 20. Surface viewer of the reference voltage controller.

mechanical neutral axis, bending creates strain within the piezoelectric element and generates voltage signal. Experimentally, if the edge of this sensor is subjected to different speeds, it can generate different values of analog voltage that depend on those speed values. The experiment was set up as shown in figure 17. The motor was run at different speeds and the output of the sensor was recorded. The speed to which the sensor is subjected equals to (Pi \* 5 \* rpm/60) mm/sec. Linear curve fitting had been applied to get the optimum modeling for the assigned slip sensor as shown in figure 18.

Fig. 18. Linear fit for slip sensor based on measured values.

The fitting parameters are recorded as follows:-

$$\mathbf{Y} = \mathbf{A} + \mathbf{B} \,\, ^\*\mathbf{X} \tag{18}$$

Where: A = 2, 45319, and B = -0, 60114

X is an independent variable that represents the object slip rate "object speed" in mm/sec. Y is a dependent variable that represents the slip sensor analog output voltage in volts.

#### **7. Gripper system controller**

Our proposed controller was developed by emulating the action of the human to handle any, object during lifting it. First, he touches the object to examine its temperature and stiffness. Then, he tries to lift it by applying small force to move it or lift it in order to acquire some information about its weight and stiffness. Then he estimates the force needed to lift this object and takes the decision if he can lift it or not. Based on these observations, two control schemes were developed with different feedback variables.

#### **7.1 First scheme controller**

During object grasping and lifting process, it is not guaranteed that the two fingers will be in contact with the object at the beginning. Hence, a pushing force will be applied by one finger (the movable finger) until complete contact. Normally, this pushing force is less than

mechanical neutral axis, bending creates strain within the piezoelectric element and generates voltage signal. Experimentally, if the edge of this sensor is subjected to different speeds, it can generate different values of analog voltage that depend on those speed values. The experiment was set up as shown in figure 17. The motor was run at different speeds and the output of the sensor was recorded. The speed to which the sensor is subjected equals to (Pi \* 5 \* rpm/60) mm/sec. Linear curve fitting had been applied to get the optimum

X is an independent variable that represents the object slip rate "object speed" in mm/sec. Y

Our proposed controller was developed by emulating the action of the human to handle any, object during lifting it. First, he touches the object to examine its temperature and stiffness. Then, he tries to lift it by applying small force to move it or lift it in order to acquire some information about its weight and stiffness. Then he estimates the force needed to lift this object and takes the decision if he can lift it or not. Based on these observations,

During object grasping and lifting process, it is not guaranteed that the two fingers will be in contact with the object at the beginning. Hence, a pushing force will be applied by one finger (the movable finger) until complete contact. Normally, this pushing force is less than

is a dependent variable that represents the slip sensor analog output voltage in volts.

two control schemes were developed with different feedback variables.

Y = A + B \* X (18)

modeling for the assigned slip sensor as shown in figure 18.

Fig. 18. Linear fit for slip sensor based on measured values.

The fitting parameters are recorded as follows:-

Where: A = 2, 45319, and B = -0, 60114

**7. Gripper system controller** 

**7.1 First scheme controller** 

the force needed to lift the object, but is a function of the object mass and its coefficient of friction. Figure 19 shows the block diagram of the first proposed controller scheme. Two integrated fuzzy controllers were built in this scheme as follows:


Fig. 19. Block diagram of the first scheme controller

Fig. 20. Surface viewer of the reference voltage controller.

Control of Efficient Intelligent Robotic Gripper Using Fuzzy Inference System 105

Fig. 22. System response for the first scheme controller: Mass=300 gm and Fpush =150 g

Fig. 23. Block diagram of the second scheme controller.

The function of the second controller is to decrease or increase the reference voltage command. The output of this controller is based on the pushing force applied on the object before grasping and lifting process. Figures 20 and 21 show the surface viewers for the two controllers in this scheme. Simulation results show the response of this scheme as shown in Figure 22.

Fig. 21. Surface viewer of the gain controller.

#### **7.2 Second scheme controller**

Three integrated fuzzy controllers were built in this scheme as shown in figure 23:-


The first controller function is to guess the acceleration of the object resulting from small applied force and to give the suitable value of reference voltage command, the second controller function is to sense the pushing force to the object before the grasping process and its output is multiplied by the first controller output, the function of the third controller is to enhance the response of the two previous controllers based on the object acceleration and the applied force feed-back.

The controllers receive the object acceleration, object acceleration rate, pushing force and the applied force as feedback variables and adjust the finger motion. The response of this scheme is shown in figure 24 which indicates a faster response and lower slippage than the first scheme controller. Also figures 25 and 26 show the effect of pushing force variation on the system response. In the case shown in figure 26, Fpush is higher than in the case shown in figure 25. So the higher value of Fpush used as feed-back to the control system leads to lower slip amount.

The function of the second controller is to decrease or increase the reference voltage command. The output of this controller is based on the pushing force applied on the object before grasping and lifting process. Figures 20 and 21 show the surface viewers for the two controllers in this scheme. Simulation results show the response of this scheme as

Three integrated fuzzy controllers were built in this scheme as shown in figure 23:-

The first controller function is to guess the acceleration of the object resulting from small applied force and to give the suitable value of reference voltage command, the second controller function is to sense the pushing force to the object before the grasping process and its output is multiplied by the first controller output, the function of the third controller is to enhance the response of the two previous controllers based on the object acceleration and

The controllers receive the object acceleration, object acceleration rate, pushing force and the applied force as feedback variables and adjust the finger motion. The response of this scheme is shown in figure 24 which indicates a faster response and lower slippage than the first scheme controller. Also figures 25 and 26 show the effect of pushing force variation on the system response. In the case shown in figure 26, Fpush is higher than in the case shown in figure 25. So the higher value of Fpush used as feed-back to the control system leads to lower

2. Increased percent controller for starter reference voltage command. 3. Enhancement controller for the starter reference voltage command.

shown in Figure 22.

Fig. 21. Surface viewer of the gain controller.

1. Guess starter reference voltage controller

**7.2 Second scheme controller** 

the applied force feed-back.

slip amount.

Fig. 22. System response for the first scheme controller: Mass=300 gm and Fpush =150 g

Fig. 23. Block diagram of the second scheme controller.

Control of Efficient Intelligent Robotic Gripper Using Fuzzy Inference System 107

Experimental work was established to verify the gripper system performance. Every part of the system was verified from the design concept, the manufacturing and control aspects. The mechanical system performance was tested and suitable refinements were performed. Sensors were calibrated and their necessary drive circuits were built. The actuator characteristics were studied in order to be taken into consideration during grasping process. Figure 26 shows the flowchart that describes the experimental scenario and proposed algorithm. Figures 27 and 28 show the system response during grasping and lifting for 1000gm object mass. Figures 27(a) and 28(a) show good performance although the start reference controller based on pushing

**8. Experimental results** 

Fig. 26. Flow chart of the proposed scenario.

Fig. 24. System response for the second scheme controller Mass = 300 gm and *Fpush* =150 g

Fig. 25. Slippage parameters and applied force.

.
