2.1 CPRF Mechanism

Two distinguishing stages exist in the grasping operation. The first is the planning stage. This period starts from the non-contact position until the moment where the finger comes into contact with the grasped object. The second one is the holding stage, which is responsible for holding the object by applying appropriate forces between the object and the finger on contact points (Buss et al., 1996). The proposed CPRF has accomplished the aforementioned two stages thanks to the design of the finger mechanism. In general, the mechanism contains three links of three joints who's angles change relatively to each other by a tendon-driven mechanism in the planning stage. The proposed VSA mechanism is placed on the other side of each joint to act as an actuator of variable stiffness to improve the grasping forces on phalanges for the holding stage.

Figure 1CPRF principle of operation (a) tendon actuating (b) VSA.

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2.1.1 Tendon-driven Mechanism

The tendon-driven mechanism is implemented to achieve force isotropy in the planning stage by using cams instead of pulleys. This tendon-driven mechanism is shown in Fig. 1a where pulley 1 is free to rotate of radius r₁, and pulley 2 is a double type free to rotate of radii r₂ and r₃, while the third one has a radius r₄ which is fixed to link (BC). Actuating the tendon, by rotating a motor in a clockwise direction, results in rotating the three links relatively during closing motion to grasp an object. Opening motion occurs by rotating the same motor in an anticlockwise direction due to the effect of tension springs of stiffness (K₁^′, K₂^′, K₃^′) shown in Fig. 1a. The relation between the lengths of finger links is set based on a real human finger. In a human finger, the mean length of the proximal phalanx approximately the sum of the lengths of intermediate phalanx and distal phalanx (Rodríguez, 2006). Thus, the relation between the lengths of CPRF links becomes as;

$$\begin{array}{}\text{(1)}& l_{\mathrm{1}}=l_{\mathrm{2}}+l_{\mathrm{3}}\end{array}$$

where l₁, l₂, and l₃ are the length of link (OA), link (AB), and link (BC), respectively. Consequently, golden ratio ϑ is used here to calculate the ratio between the lengths of two consecutive links (Rizk, 2007; Dandash et al., 2011; Ask, 2016);

$$\begin{array}{}\text{(2)}& l_{\mathrm{3}}=\mathit{\vartheta }{l}_{\mathrm{2}}={\mathit{\vartheta }}^{\mathrm{2}}{l}_{\mathrm{1}}\end{array}$$

assuming that the phalanges contact the object along their entire length. Hence, the pressure, i.e. the pressure produced by contact forces on the length of finger links, is; To add a, b, c to the numbering:

$$\begin{array}{}\text{(3a)}& p_{\mathrm{1}}={\displaystyle \frac{f_{\mathrm{1}}}{b{l}_{\mathrm{1}}}}\end{array}$$

$$\begin{array}{}\text{(3b)}& p_{\mathrm{2}}={\displaystyle \frac{f_{\mathrm{2}}}{b{l}_{\mathrm{2}}}}\end{array}$$

$$\begin{array}{}\text{(3c)}& p_{\mathrm{3}}={\displaystyle \frac{f_{\mathrm{3}}}{b{l}_{\mathrm{3}}}}\end{array}$$

where b is the width of the finger. In order to get a uniform contact pressure during grasping, Eq. (3a, b) is equalized. In this way;

$$\begin{array}{}\text{(4)}& {\displaystyle \frac{f_{\mathrm{1}}}{b{l}_{\mathrm{1}}}}={\displaystyle \frac{f_{\mathrm{2}}}{b{l}_{\mathrm{2}}}},f_{\mathrm{1}}={\displaystyle \frac{l_{\mathrm{1}}}{l_{\mathrm{2}}}}{f}_{\mathrm{2}}\end{array}$$

from Eq. (2), the ratio between l₁ and l₂ is;

$${\displaystyle \frac{l_{\mathrm{1}}}{l_{\mathrm{2}}}}=\mathit{\vartheta },$$

hence, Eq. (4) becomes;

$$\begin{array}{}\text{(5)}& f_{\mathrm{2}}={\displaystyle \frac{\mathrm{1}}{\mathit{\vartheta }}}{f}_{\mathrm{1}}\end{array}$$

also, Eq. (3b, c) is equalized to get a uniform contact pressure. Thus;

$$\begin{array}{}\text{(6)}& {\displaystyle \frac{f_{\mathrm{2}}}{b{l}_{\mathrm{2}}}}={\displaystyle \frac{f_{\mathrm{3}}}{b{l}_{\mathrm{3}}}},f_{\mathrm{2}}={\displaystyle \frac{l_{\mathrm{2}}}{l_{\mathrm{3}}}}{f}_{\mathrm{3}},\end{array}$$

from Eq. (2), the ratio between l₂ and l₃ is;

$${\displaystyle \frac{l_{\mathrm{2}}}{l_{\mathrm{3}}}}=\mathit{\vartheta },$$

hence, Eq. (6) becomes;

$$\begin{array}{}\text{(7)}& f_{\mathrm{3}}={\displaystyle \frac{\mathrm{1}}{\mathit{\vartheta }}}{f}_{\mathrm{2}}.\end{array}$$

Supporting distributed pressure on the grasped object, to avoid the damage to the grasped object, is achieved by considering the force isotropy between contact forces in Eqs. (5) and (7). These two equations are used later in the geometry design of finger in Sect. (2.2) to enable the configuration motion of finger contact the grasped object with force isotropy property.

Table 1Physical properties for the torsion spring of material stain steel.

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2.1.2 VSA Mechanism

The basic idea of the suggested VSA mechanism is obtained from the design equations of torsion spring. A torsion spring of properties listed in Table 1 is mounted on the joint shaft (O: MCP joint, A: PIP joint, and B: DIP joint). If one of its ends is fixed with the link of the robot finger and the other end is free to rotate through a pulley as shown in Fig. 1b, by changing the angle of the pulley by tendon through a motor, the mean diameter D_m of the spring is reduced according to the following equation (Shigley and Mischke, 2004);

$$\begin{array}{}\text{(8)}& D_{\mathrm{m}}={\displaystyle \frac{D_{\mathrm{1}}{N}_b}{N_b+\mathrm{\Delta }\mathit{\theta }}},\end{array}$$

assuming i the index of joint (where $i=\mathrm{1},\mathrm{\dots },\mathrm{3}$), the stiffness rate per degree is changed;

$$\begin{array}{}\text{(9)}& k_i={\displaystyle \frac{\mathit{\pi }E{d}^{\mathrm{4}}}{\mathrm{64}\cdot \mathrm{180}{D}_{\mathrm{m}}{N}_{\mathrm{A}}}},\end{array}$$

where Δθ is the difference between the angle θ of the link and the free end side of the torsion spring θ^′ shown in Fig. 1b. The link is considered fixed because in the control approach the stiffness of the VSA is adjusted only in the hold position. During change the stiffness, the supplied torque by VSA at each joint becomes;

$$\begin{array}{}\text{(10)}& T_i=k_i\mathrm{\Delta }\mathit{\theta }.\end{array}$$

Hence, tuning the stiffness of VSA gives rise to a corresponding torque as shown in Fig. 2.

Figure 2Supplied torque by VSA corresponding to the change of stiffness with respecting to the deflection.

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2.2 CPRF Design

Geometric model of Fig. 1a with input and output forces is presented in Fig. 3 and its parameters are detailed in Table 2 (where $i=\mathrm{1},\mathrm{\dots },\mathrm{3})$. Geometric parameters of mechanism parts are set to avoid undistributed contact forces on phalanges. Specifically, in the kineto-static analysis, contact forces are derived here from the input and output powers of the CPRF. Then, these contact forces are substituted in Eqs. (5) and (7) in order to find the relations between radii of pulleys which achieve force isotropy. Next, some pulleys are replaced with cams so that the relative motion between phalanges is regulated to reach the grasped object with close contact forces. Finally, the profile of cams is obtained by some mathematical calculations.

Figure 3CPRF geometric model with input and output forces.

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Let P_in and P_out denote the input and output power to the robot finger, respectively. These powers are obtained as;

where

equalizing Eqs. (11) and (12), contact forces become;

where

Table 2Parameters of CPRF analysis.

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Figure 4Geometrical analysis of cam 4 profile.

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The springs in the tendon-driven mechanism have low stiffness when all phalanges make contact with the grasped object, compared with the actuation torque. In addition, the actuation torque has to remain constant to have an isotropic design. Therefore, the action of the springs is negligible in the kineto-static analysis of tendon-driven mechanisms (Krut, 2005; Birglen et al., 2008; Dandash et al., 2011). By ignoring the effect of springs, the contact forces in Eqs. (13–15) become;

substituting Eqs. (17) and (18) into Eq. (7), to find the relation between radii that gives force isotropy, yields the ratio between r₃ and r₄;

the above equation maps the profile of cam 4. For a constant radius r₃, the profile of cam 4 is obtained by geometrical analysis of Fig. 4 with some calculations. Assuming;

and rearranging Eq. (20) in term of Q, we obtain;

from Fig. 4, β is;

substituting Eq. (20a) in this formula, yields;

selecting the vector u parallel to the tendon path between points (H₃H₄) and the vector v parallel to the path between point (H₄) and joint (B), we get;

assume J an arbitrary point on the tendon, then;

using the vectors in Eq. (22a–d), Eq. (26) becomes;

profile of cam 4 is determined by values of u that satisfies the following determinant matrix (Dandash et al., 2011);

the elements of the determinant matrix are obtained from Eq. (24a, b);

then, the determinant in Eq. (28) is calculated as follow;

rearranging the Eq. (29) in term of u, we get;

referring to Eqs. (20b) and (21);

In this way, the profile of cam 4 in Eq. (24a, b) is obtained as;

Figure 5Geometrical analysis of cam 2 profile.

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The next step is to obtain the profile of cam 2. Getting the profile of cam 2 is more complicated than cam 4 profile because cam 2 is free to rotate, while cam 4 is fixed to distal phalanx. Since cam 2 is free to rotate on the joint (A); therefore, we should find a relation between the free rotation of cam 2 and the rotation of link 2. Assuming cam 2 rotates with an angle θ_cam 2 as shown in Fig. 5, hence;

let;

then;

substituting Eqs. (16) and (17) into Eq. (5), to find the relation between radii that gives force isotropy, yields the ratio between r₁ and r₂;

where;

the ration between pulleys in Eq. (30) is a function of N₁, l₁, l₂, l₃, θ₂, θ₃, and ϑ. Eq. (30) maps the profile of cam 2. For a constant radius r₁, the profile of cam 2 is obtained by geometrical analysis of Fig. 5 with some calculations as follows:

let;

then merging Eq. (31) with Eq. (30), yields;

and

Figure 6Cam on DIP joint (a) cam 4 profile (b) CAD drawing.

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As shown in Fig. 5, the angle between link (OA) and the tendon is;

let J₁ the nearest point of the tendon to the joint (A);

let J₂ be any point of the tendon;

then;

by applying the same procedure in deriving the path of cam 4, the profile of cam 2 is obtained by λ. Assume;

according to Eq. (35a, b);

substituting these two formulas in Eq. (36) and after calculating of the determinant matrix, we get;

to find $\frac{\mathit{\delta }\mathit{\gamma }}{\mathit{\delta }{\mathbf{r}}_{\mathbf{2}}}$ and $\frac{\mathit{\delta }{\mathbf{r}}_{\mathbf{2}}}{\mathit{\delta }{\mathit{\theta }}_{\mathrm{cam}\mathrm{2}}}$, r₂ is obtained from Eq. (34);

Figure 7Double cam pulley on PIP joint (a) cam 2 profile (b) CAD drawing.

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Table 3Parameters of design cam 2 and cam 4.

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thus;

according to Eq. (31);

hence;

referring to Eqs. (32) and(33);

now substituting Eqs. (38) and (39) in Eq. (37), yields;

Figure 8CPRF mechanical parts (a) CAD drawing (b) produced Prototype.

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Hence, cam 2 profile in Eq. (35a, b) is obtained as;

Figure 9CPRH System (a) Diagram of components (b) Hardware architecture of the electronic and drive system.

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The profile of cam 4 from Eq. (27a, b) is calculated and designed in the CAD drawing as shown in Fig. 6 for a constant radius of pulley3 4 mm, maximum distal rotation angle 90^∘, and length of link 1 (Proximal), link 2 (Intermediate), and link 3 (Distal) 50, 30.902, and 19.098 mm, respectively. The lengths of the intermediate and distal phalanges are calculated using golden ratio relation between links in Eq. (2) from the length of the proximal phalanx. On the other hand, the profile of cam 2 is calculated and also designed in CAD drawing by using Eq. (41a, b) as shown in Fig. 7 for pulley1 radius equal to 4 mm and radius of the basic pulley of cam 2 equal to 1.5 mm with maximum intermediate link angle of rotation 90^∘. All the described parameters of design cam 2 and cam 4 are listed in Table 3. Implementing these numerical values and geometry design, the CAD of CPRF parts are drawn and assembled as shown Fig. 8a. Then, they are manufactured by a 3-D printer and assembled together with torsion springs to obtain the CPRF prototype shown in Fig. 8b.

Figure 10The prototype of robot hand (a) 3-D CAD drawing (b) CPRH (c) CPRF.

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3.1 Sensorimotor System

Figure 11Workspace of the designed CPRF for seven situations with 10^∘ step between each one.

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A suitable sensorimotor layout is proposed, designed, and programmed with its computer interface circuit to sense the grasped objects and actuate the mechanical parts of the designed CPRF in CPRH. The overall layout is shown in Fig. 9a, in which, the motor of the tendon-driven mechanism is controlled by force sensors which in turn adjust the stiffness of the VSAs. A Force Sensitive Resistor (FSR) sensor is used to sense touch on the phalanges. The sensor type (FSR 402 Short) of 15.24 mm diameter is applied for proximal phalanx and type (FSR 400 Short) of 6.35 mm diameter is applied for intermediate and distal phalanges (Pololu Force Sensing Resistor, 2018). The FSR sensor changes its resistance depending on the magnitude of the force applied to its surface. In order to be able to read the sensor signals, an electronic circuit is designed that pinned the analog signal from a voltage divider circuit of a resistance 10 kΩ to the Arduino 2560 microcontroller board analog signal pins (A0, … , A5). Additionally, the designed electronic circuit assists in producing more output changes with respect to fewer changes of FSR resistance to overcome the nonlinearity of FSR sensors. To obtain proper experimental data, it was important to calibrate the force sensors employed in the robot finger. For all FSR 400 series sensors used, obtaining force unit from the resistance of the sensor is implemented dependent on the number of analogue to digital converter (ADC) bits and voltage divider circuit. Using: (1) the Arduino 2560 microcontroller board of 10 bits; and (2) the range of mapping voltage between 0–5000 mV, we get;

where V_FSR and V_analog are the voltage across the FSR sensor and the analogue voltage of FSR sensor, respectively. Considering the voltage divider circuit, we obtain;

Figure 12Monitoring touch performance of force signals.

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Where R_FSR and G_FSR are the resistance and the conductance of FSR sensor, respectively. In the designed electronic circuit of the CPRF, V_cc=5 V and R=10 kΩ. Converting the signal of sensors to force in Newton (N) unit is obtained using Eq. (42d), the relation between force and resistance mentioned in the datasheet of the used sensor i.e. FSR 400 series sensor, and the following algorithm;

The grasped object is detected when the signal of the sensor is above zero. Control servo motors are done by connecting signals of servo motors to the PWM on the microcontroller board. Fig. 9b presents the overall view of the electronic hardware system. A Simulink model as a software tool is built in MATLAB to read the signals of the force sensors and actuate the motion of the motors via computer. This MATLAB program is used to test the control algorithms and the performance of the designed finger in a realistic way.

Figure 13Block diagram of the CPRF control system.

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3.2 CPRH Developing

The design of the mechanical parts of the CPRH includes hand base, palm, two CPRFs, and an electronic hardware box. The hand base contains motors to actuate the motion of the CPRFs and tune VSAs. The CPRF motion is actuated by one tendon through a servo motor type (SH-0253) for closing and opening motions, the stiffness of each VSA is controlled by tendon through a servo motor type (SG90) that resulted in driving each finger by four motors. FSR sensors are covered by a pad in order to assist diffusing touch across the sensor region and enhance the grasp performance due to its coefficient of friction and soft property. The final CPRH prototype system is manufactured as shown in Fig. 10 where all the mechanical parts of the 3-D drawing are produced by the 3-D printer.

Figure 14Fuzzy inputs and outputs (a) relations (b) Prepositions.

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Tests are done by actuating the finger and pressing on phalanges. Actuating servo motor type SH-0253 from 0 to 70^∘ resulted in moving the CPRF from its initial to a final position during closing motion without a grasped object as shown in Fig. 11. A second test is done to monitor the calibrated force signals in Newton unit during contact when the applied force is varied. The source of the applied force is the human fingertip as shown in Fig. 12. The contact on phalanges can be sensed simultaneously at the same time with a zero value when there is no touch i.e. without noise (see hyperlink of “Movie 1 CPRF” in the Appendix).

Figure 15Fuzzy sets of inputs and outputs.

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4.1 MIMO Fuzzy Controller

In the practical application of CPRF, the factors that affect the grasping are complex and involve tendon mechanism, multi-VSAs, interactional contact between the phalanges and the grasped object, response time of sensors and servo motors, and CPRF dynamics. Since the majority of these factors are variant with time and nonlinear, calculating the exact mathematical model of the CPRF is not easy. As a result, traditional control methods such as PID method lack providing accurate grasp control. However, the fuzzy control technique can be applied to real applications dependent on knowing an intuitive realization of the best way to control the system (Passino and Yurkovich, 1997). A special MIMO fuzzy controller is designed and applied to the CPRF control system shown in Fig. 13. The controller is a MIMO that sinks the indication from the force sensors, assesses them, and produces a conclusion according to its predefined rules to formulate output torque values in each VSA.

The action of the controller is qualified by fuzzy rules with the relation of input data mapping and proposition of output, the linguistic variables are;

FSR_Force 1 = {low, medium, high}
FSR_Force 2 = {low, medium, high}
FSR_Force 3 = {low, medium, high}

VSA_Torque 1 = {low, medium, high}
VSA_Torque 2 = {low, medium, high}
VSA_Torque 3 = {low, medium, high}

The input variables and output variables have 27 relations R_ijk and 27 propositions P_ijk, respectively. The relations and propositions are expressed in a matrix form as shown in Fig. 14, where $i,j,k=\mathrm{1},\mathrm{\dots },\mathrm{3}$; Fi = FSR_Force i; Ti = VSA_Torque i. Fuzzy rule are defined now by IF relation then proposition statements as;

The rules, there are 27 rules that determine the values of outputs, are specified according to the designed relations and proposition matrix shown in Fig. 14. To clarify the designed rules, let us assume the conditions of force sensors are;

FSR signal 1 is low, FSR signal 2 is high, FSR signal 3 is low

In this case, as shown in Fig. 14, the rule is set as;

if (FSR Force 1 is low) and (FSR Force 2 is high) and (FSR Force 3 is low) then (VSA Torque 1 is low) and (VSA Torque 2 is high) and (VSA Torque 3 is low)

Another example is assumed when the conditions of force sensors are;

FSR Force 1 is high, FSR Force 2 is low, FSR Force 3 is low

Then, as shown in Fig. 14, the rule is set to;

if (FSR Force 1 is high) and (FSR Force 2 is low) and (FSR Force 3 is low) then (VSA Torque 1 is high) and (VSA Torque 2 is low) and (VSA Torque 3 is low)

In the same way, the other rules are set according to the state of the input force sensors. The input forces of the controller and the output torques are decomposed into fuzzy sets (low, medium, high) by triangular membership functions of range 〈a   b〉 and nucleus 〈c   d〉;

Matching to the range of FSR signal of 10-bit data from 0 to 1023, the domain of the input force sensor in Newton unit is set from 0 to 10 N depending on the properties of the applied sensors FSR400 series. The range of the output torque is set depending on the designed VSA. The control strategy is assumed from Δθ equal 0 to 270^∘ which results in changes of mean diameter and stiffness from (5.3 mm, 0.2144 N mm degree⁻¹) to (4.627 mm, 0.5512 N mm degree⁻¹) according to Eqs. (8) and (9). Hence, the torque by VSA is supplied in joint space according to Eq. (11) from 0 to 2.5973 N mm.

The plot of the fuzzy sets is presented in Fig. 15, the fuzzy is implemented using Mamdani with the center of gravity defuzzification method of implication minimum operator and aggregation maximum operator. The first step of the fuzzification process is to obtain the crisp of the forces sensors and to determine how these inputs belong to the fuzzy sets. Then, the fuzzified inputs using Eq. (48) is taken and applied to the antecedents of the rules. Since our designed fuzzy controller rule has various antecedents operator, the AND or OR operator is implemented to get the value of the antecedent evaluation. Then, this value is used to the followed membership function. The fuzzy operation (OR) union maximum operator is used to find the disjunction of the rule antecedents, as below;

and the fuzzy operation (AND) intersection minimum operator is used to finding the conjunction of the rule antecedents, as bellow;

4.2 Optimized MIMO Fuzzy Controller

The designed fuzzy controller suffered from undistributed VSA torques in a proper manner. In this situation, there was a large difference between the values of VSA torques which can lead to damage the grasped object. Hence, the boundaries of the input membership functions should be modified to enhance the performance of the controller. Traditional trial and error techniques do not provide optimal solutions. Consequently, a genetic algorithm is applied here to get the optimum boundaries of membership functions so that the difference between the VSA-torques is minimized. A genetic algorithm is an advanced technique for complex issues that realizes optimum value for several systems (Gen and Cheng, 1997). The tuning process of membership boundaries via genetic algorithm is performed using MATLAB. The code takes the calculated data from the designed tradition fuzzy controller Simulink model to compute the difference between the VSA torques. The planning for the implemented genetic algorithm is as follows;

• Population: the generated population includes the individuals which represented in our case the boundary of the input membership function as;

  $$x\left(\stackrel{\mathrm{ˇ}}{i},\stackrel{\mathrm{ˇ}}{j}\right)$$

  where $\stackrel{\mathrm{ˇ}}{i}$ and $\stackrel{\mathrm{ˇ}}{j}$ are the index of boundary and contact force, respectively. In the designed fuzzy controller, as shown in Fig. 15, there are three membership functions (low, medium, high) and three contact forces (Force 1, Force 2, Force 3). So, $\stackrel{\mathrm{ˇ}}{i}=\stackrel{\mathrm{ˇ}}{j}=\mathrm{1},\mathrm{2},\mathrm{3}$ .

• Fitness function: to optimize the performance of the fuzzy controller, it is important to specify the fitness function. The aim of our fuzzy controller is to supply appropriate close values of VSA-torque during grasping. Consequently, the fitness function is defined as

  $$\begin{array}{ll}{\displaystyle }& {\displaystyle }\mathrm{Fitness}\mathrm{\_}\mathrm{Function}=\\ \text{(46)}& {\displaystyle }& {\displaystyle }\mathrm{absolute}(\mathrm{Torque}\mathrm{1}-\mathrm{Torque}\mathrm{2}-\mathrm{Torque}\mathrm{3})\end{array}$$

  The adjusting process of boundaries is limited by the physical properties of our force sensors and VSAs. Thus, the limits of the applied genetic algorithm are set as follows;

  $$\begin{array}{ll}{\displaystyle }& {\displaystyle }\mathrm{Force}\stackrel{\mathrm{ˇ}}{j},<\mathrm{10},\\ {\displaystyle }& {\displaystyle }\mathrm{Torque}\stackrel{\mathrm{ˇ}}{j}<\mathrm{2.5973},\end{array}$$

• Genetic algorithm parameters: The genetic algorithm is set with the following values; size of population: 90 and number of generation: 40.

The result of the optimization process of the fuzzy controller in term of the new triangular membership parameters is shown in Fig. 16.

Figure 16Optimized Fuzzy sets of inputs.

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To explain the advancement of the optimized fuzzy controller, the traditional fuzzy controller explained in Sect. 4.1 and optimized fuzzy controller are tested under the contact force touching scenario. The simulation time is set to 15 s. Note that the performance of the controllers is examined under contact forces shown in Fig. 17. Results are shown in Fig. 18 with the VSA-torque compared between Fuzzy and optimized fizzy controllers.

Figure 17Contact force on phalanges scenario.

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Figure 18Traditional optimized VSA-torques.

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To further explain the distinction between the two controllers, the absolute difference between the VSA torques in each controller of data presented in Fig. 18 is plotted together in Fig. 19. It can be noticed that there is a distinctive difference between the obtained VSA-torques of the two fuzzy controllers. The optimized fuzzy controller has preferred the values of VSA-torques. In turn, the CPRF grasping is enhanced with an appropriate controller in addition to the functionality of the proposed adjustable stiffness tendon-driven mechanism.

Figure 19The difference between VSA-torques.

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4.3 Operation Control

A simple control algorithm is defined to organize the finger system into many orders and sets. The algorithm is allowed to sense the environment, actuate the finger, and adjust the VSAs according to sensations as shown in Fig. 20. The FSRs analog signals i.e. force sensing in Newton unit are used principally for actuating the finger, adjusting the VSA-torque, and starting the optimized fuzzy controller. Hence, the action of the finger is divided into motion and grasp force spectrum. Motion happens when the system does not sense a grasped object. In the moment of detecting the grasped object, the optimized fuzzy controller is activated to start the grasping phase. Testing with a threshold force equal to 2 N is presented in Table 4. This table explains the response of the VSAs to different touch values over the control algorithm. It can be distinctly seen that the amount of VSA torque varies considerably when there is a touch variation value on the phalanx which is directly in connection with that VSA. For example, according to test 2 and test 3, the finger stopped its motion when the force F1 reached the threshold value. In the same time, the torque of VSA1 increased due to increasing the force on proximal phalanx which is directly connected to it.

Figure 20Program flowchart of the control algorithms for each finger.

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