**4.3 Control of a single tactile transducer**

For the sake of clarity we firstly present a method for the control of one transducer and extend the concept to multiple transducers in the following section. The scheme for controlling the current applied to a single transducer is shown in Fig. 6. The solution is based on current Pulse Width Modulation (PWM) technique. The represented circuit allows applying a pulsed current that can assume any wanted average value programmed by a PWM output of a microcontroller (named as uP in the figure).

Referring to the scheme in Fig. 6, the coil is schematized by an RL series circuit. The PWM output of the microcontroller modulates the current by mean of a the signal S through a MOSFET. When the MOSFET is turned on (ON phase), the current flows into the coil and also into the capacitor. When the MOSFET is turned off (OFF phase), the coil current is supplied by the capacitor. The capacitor is introduced in order to limit the current ripple.


Fig. 6. Scheme for the PWM control of a single tactile transducer

During the OFF phase, the function of the coil current is given by transient behavior of the RLC-series circuit, characterized by the natural frequency, damping ratio and time constant

One of the issues regarding the integration of a tactile array on a force feedback device is the bulkiness and disturbances introduced by the large number of connectors and signals that are needed for the independent control of each transducer of the tactile array. For getting around this issue the control electronic board should be integrated on the robotic structure as near as possible to the transducers. This solution is necessary for reducing the impact of the cabling on the robotic structure, but also it imposes constraints on the encumbrance of the electronic. For this reason specific customized solutions have to be adopted for the control of each transducer. Here we present a possible approach based on the strategy for controlling the status of the pixels in a LCD display called active matrix addressing. This strategy can be implemented in any *n by m* array of actuators but we show an implementation that is referred to the solenoid array described in the previous section.

For the sake of clarity we firstly present a method for the control of one transducer and extend the concept to multiple transducers in the following section. The scheme for controlling the current applied to a single transducer is shown in Fig. 6. The solution is based on current Pulse Width Modulation (PWM) technique. The represented circuit allows applying a pulsed current that can assume any wanted average value programmed by a

Referring to the scheme in Fig. 6, the coil is schematized by an RL series circuit. The PWM output of the microcontroller modulates the current by mean of a the signal S through a MOSFET. When the MOSFET is turned on (ON phase), the current flows into the coil and also into the capacitor. When the MOSFET is turned off (OFF phase), the coil current is supplied by the capacitor. The capacitor is introduced in order to limit the current ripple.

During the OFF phase, the function of the coil current is given by transient behavior of the RLC-series circuit, characterized by the natural frequency, damping ratio and time constant

**4.2.2 Electronics and control** 

**4.3 Control of a single tactile transducer** 

PWM output of a microcontroller (named as uP in the figure).

Fig. 6. Scheme for the PWM control of a single tactile transducer

$$
\rho\_{n, \mathrm{OFF}} = \frac{1}{\sqrt{\mathrm{LC}}} ; \quad \quad \mathbb{X}\_{\mathrm{OFF}} = \frac{R}{2} \sqrt{\frac{\mathrm{C}}{L}} ; \quad \quad \pi\_{\mathrm{OFF}} = \frac{2L}{R} . .
$$

During the ON phase, the transfer function which expresses the coil current respect to the supply voltage is the following

$$\frac{I\_L}{V\_{CC}} = \frac{1}{R\_0L\,\mathrm{Cs}^2 + \left(R\_0RC + L\right)\mathrm{s} + R\_0 + R}$$

in which the typical MOSFET on-resistance is considered inside the term R0. The natural frequency, the damping ratio and the time constant are:

<sup>0</sup> , , 1 1 *n ON n OFF R R* ; <sup>0</sup> 0 1 1 *ON OFF L R RC R R* ; 0 1 1 *ON OFF L R RC* ;

A necessary condition for limiting the variation of current through the coil during a PWM cycle is to dimension the capacitor C and the resistor R0 imposing a time constants of the OFF phase circuits larger enough than the period of the PWM cycle.

Assuming that this requirement is satisfied, it's possible to find a simplified relation between the coil current and the duty cycle of the PWM signal. Making the assumption that *VC* is a constant voltage applied to the capacitor, the current *iC* flowing into the capacitor during the ON phase is given by

$$i\_{C,ON} = \frac{V\_{CC} - V\_C}{R\_0} - \frac{V\_C}{R}$$

The supplied electrical charge can be written as:

$$Q\_{ON} = T\_{ON} \frac{1}{C} \left(\frac{V\_{CC} - V\_C}{R\_0} - \frac{V\_C}{R}\right)$$

During the OFF phase, the above quantities can be expressed as follow

$$i\_{C,OFF} = \frac{V\_{\mathbb{C}}}{R} ; Q\_{OFF} = T\_{OFF} \frac{1}{C} \frac{V\_{\mathbb{C}}}{R} ; :$$

Indicating with α and *TPWM* respectively the duty cycle and the period of the PWM signal,

$$\begin{cases} T\_{ON} = a \cdot T\_{PV\mathcal{M}} \\ T\_{OFF} = (1 - a) \cdot T\_{PV\mathcal{M}} \end{cases}$$

When the frequency content of variation of the imposed average current is much lower than the PWM frequency we can assume that the charge during the two phases are identical. We can than calculate the duty cycle for obtaining an average coil current *iL* :

On the Integration of Tactile and Force Feedback 67

element *Bij* (that indicates the *ij*-esim solenoid) it is sufficient to activate the row *i* by powering the gates of the associated miniature p-MOSFETs (digital output *Ri* is set to logic 1) and to modulate the current by setting the correspondent duty cycle of the PWM signal

Referring to Figure 8, the algorithm for controlling the *m+n* digital signal in order to apply



The limitation of the maximum duty cycle for each coil (due to the limited period of time for the modulation) requires a higher impulse of the supplied current (approximately *m* time higher in comparison to the case of a single transducer). This produces higher disturbances in the coil current, as shown in 0 where the coil current are estimated as described in section 4.1 but limiting the maximum duty cycle to 0.2 (that is, considering the case of our array of 5

According to a first set of preliminary tests, despite the fact that the current ripple seems to be quite large (Fig. 9), its effect on the output of the tactile transducer is not so relevant. Probably the mass and the friction of the electromechanical solenoid acts as a filter for frequencies of 10kHz and the resulting displacement of the plunger is extremely reduced.

the required current values for the all transducers of the tactile array is the following:

Fig. 8. Scheme of the control electronics of a 3 x 3 array of pins.

indicate in formula (3) is equal to *αmax = 1/m*.

which control the column *j*.

row is *TR = TH /m*;

row).

$$\alpha = \frac{\mathcal{R}\_0 \cdot i\_L}{V\_{\text{CC}} - \mathcal{R} \cdot i\_L}$$

Supposing that the supply voltage *VCC* is fixed, by the previous equation it's also possible to define the relation between the resistance *R0* and the maximum coil current *iL,max* :

$$\dot{a}\_{L,\text{max}} = V\_{\text{CC}} \frac{a\_{\text{max}}}{a\_{\text{max}} \cdot R + R\_0}$$

Where *αmax* is the maximum duty cycle of the PWM signal. In particular, if *αmax* = 1, we obtain

$$i\_{L, \text{max}} = V\_{CC} \frac{1}{R + R\_0}$$

#### **4.3.1 Design and simulation**

For testing the current modulation performances of the proposed technique, the circuit shown in Fig. 6 has been simulated using Simulink (Matlab). The adopted system parameters for the simulation are reported in the same figure. The PWM switching frequency is fixed at 10kHz. A sine wave with frequency of 100Hz, amplitude of 0.6A and an offset of 0.3A is chosen as the average current to be imposed. The resistance R0 has been dimensioned for obtaining the maximum current of 0.6A with a duty cycle *αmax* = 1. In Fig. 7, the currents flowing through the coil by using three different capacitors of 100µF and 33µF are reported.

Fig. 7. Current with cap of C of 100µF (a) and 33µF (b).

#### **4.4 Control of the complete tactile array**

The extension of the single actuation scheme proposed in the previous section to an *m x n* array of transducers imposes the use of a microcontroller able to generate *m x n* independent PWM signals and *m x n* wired connections.

In order to obtain simple hardware architecture, an actuation solution base on matrix addressing technique has been analyzed. In this case, only *m + n* control signals are required. The PWM signals are divided in into row signals and column signal. The row signals determine the row that is addressed: all of the *m* transducers on the selected row are addressed simultaneously. When a row is selected, each signal of the *n* columns should be individually controlled for modulating the respective coil current.

This type of addressing is similar to the strategy for controlling the status of the pixels in a LCD display called *active matrix addressing*. In Fig. 8, a scheme for controlling three rows and three columns of the tactile array is shown. For controlling the current of the generic

max ,max

Where *αmax* is the maximum duty cycle of the PWM signal. In particular, if *αmax* = 1, we obtain

For testing the current modulation performances of the proposed technique, the circuit shown in Fig. 6 has been simulated using Simulink (Matlab). The adopted system parameters for the simulation are reported in the same figure. The PWM switching frequency is fixed at 10kHz. A sine wave with frequency of 100Hz, amplitude of 0.6A and an offset of 0.3A is chosen as the average current to be imposed. The resistance R0 has been dimensioned for obtaining the maximum current of 0.6A with a duty cycle *αmax* = 1. In Fig. 7, the currents flowing through the

(a) (b)

The extension of the single actuation scheme proposed in the previous section to an *m x n* array of transducers imposes the use of a microcontroller able to generate *m x n* independent

In order to obtain simple hardware architecture, an actuation solution base on matrix addressing technique has been analyzed. In this case, only *m + n* control signals are required. The PWM signals are divided in into row signals and column signal. The row signals determine the row that is addressed: all of the *m* transducers on the selected row are addressed simultaneously. When a row is selected, each signal of the *n* columns should be

This type of addressing is similar to the strategy for controlling the status of the pixels in a LCD display called *active matrix addressing*. In Fig. 8, a scheme for controlling three rows and three columns of the tactile array is shown. For controlling the current of the generic

*R R*

Supposing that the supply voltage *VCC* is fixed, by the previous equation it's also possible to

define the relation between the resistance *R0* and the maximum coil current *iL,max* :

*L CC i V*

,max

coil by using three different capacitors of 100µF and 33µF are reported.

Fig. 7. Current with cap of C of 100µF (a) and 33µF (b).

individually controlled for modulating the respective coil current.

**4.4 Control of the complete tactile array** 

PWM signals and *m x n* wired connections.

**4.3.1 Design and simulation** 

*L CC i V*

0 *L CC L R i V Ri*

max 0

1

*R R*

0

element *Bij* (that indicates the *ij*-esim solenoid) it is sufficient to activate the row *i* by powering the gates of the associated miniature p-MOSFETs (digital output *Ri* is set to logic 1) and to modulate the current by setting the correspondent duty cycle of the PWM signal which control the column *j*.

Fig. 8. Scheme of the control electronics of a 3 x 3 array of pins.

Referring to Figure 8, the algorithm for controlling the *m+n* digital signal in order to apply the required current values for the all transducers of the tactile array is the following:


The limitation of the maximum duty cycle for each coil (due to the limited period of time for the modulation) requires a higher impulse of the supplied current (approximately *m* time higher in comparison to the case of a single transducer). This produces higher disturbances in the coil current, as shown in 0 where the coil current are estimated as described in section 4.1 but limiting the maximum duty cycle to 0.2 (that is, considering the case of our array of 5 row).

According to a first set of preliminary tests, despite the fact that the current ripple seems to be quite large (Fig. 9), its effect on the output of the tactile transducer is not so relevant. Probably the mass and the friction of the electromechanical solenoid acts as a filter for frequencies of 10kHz and the resulting displacement of the plunger is extremely reduced.

On the Integration of Tactile and Force Feedback 69

The geometrical model adopted is based on FEM because they have been proved to be able to map and represent physical properties of material in a better way. In particular the textile is represented by thin triangular shells along the application to cloth simulation by Etzmuss (Etzmuss, Keckeisen, & Strasser, 2003). The physical forces employed are the stretch and bend as expressed by the elastic tensor. These forces are computed from the deformation of the triangle against its original condition but such computation is quite expensive. For this reason we employed co-rotated triangles in which the triangle deformation is expressed by a combination of a rotation and a deformation of the planar version of the triangle. The overall equation of motion of the nodes of the triangles takes into account these forces in addition to external forces like gravity. The node equation is then integrated using implicit Euler that provides more precise simulation at the cost of resolution of a system of equations. This system of equation is solved using a preconditioned conjugate gradient in

The collision method employed is based on the contact between two spherical proxies of the subject fingers and the vertices of the textile. Each collision makes the textile instantly to move to avoid the collision and then the collision is implemented as a constraint that blocks the motion of the node toward the proxy sphere. This constraint on the node is taken into account in the system resolution by means of a modified preconditioned conjugate model using the filtering approach introduced by Baraff (Baraff & Witkin, 1998). This representation of constraints allows implementing also generic constrained nodes to hang

The haptic feedback module runs in a separate thread and it has two objectives: provide feedback of interaction among the finger proxies, and the interaction with the textiles. The finger feedback is provided by means of a damped virtual spring that is activated when the two proxies are below a given threshold. This spring is necessary to compensate the effective size of the gimble that surround the fingers. When each proxy sphere collides with the nodes of the textile it moves the node outside the sphere. The overall force on the proxy is made by two components one impulsive that accounts for the instantaneous motion of the textile, while the other is the pressure applied by the node on the sphere. This pressure of the node on the proxy can be measured as the action performed by the node over the constraint that is effectively the residual of the iterative resolution of the system. This approach is different with respect the previous work (Fontana et al., 2007) the haptic force

The model described so far does not take into account two related aspects of the interaction: friction and textile compression. Without introducing textile compression friction emerges from the forces exchanged between the proxy and the nodes due to the work of the constraints of the contacting nodes. Effectively this model produces small exchanged forces due to the small work of these constraints. An additional contribution to the normal component is caused by the compression of the textile. The FEM model does not take into

**4.5.1 Simulation** 

**4.5.2 Collision** 

the textile in a given position.

**4.5.3 Proxy and haptic feedback** 

was based on a penalty method.

which the preconditioning is the block diagonal.

Fig. 9. Coil current of a matrix with 5 row and with capacitance *C* of 100µF (a) and 33µF (b).
