**4.2. BaTboT: a biologically-inspired bat-like aerial robot**

BaTboT is a bio-inspired bat robot that uses Shape Memory Alloys (SMAs) as artificial muscles for powering the morphing motion of the wings. The morphing motion is related to the capacity of the robot to modulate its wings by contracting and extending the membrane in sync with the flapping motion. It is precisely this characteristic what makes biological bats more agile to maneuver than any other flying creature within the same Reynolds number range (103 <sup>−</sup> 104) [66], [22]. In addition, biological studies in [32], [58] have revealed that real bats are able to maneuver because of the inertial changes produced by the wings' modulations. Attempting to mimic this functionality using an artificial counterpart -BaTboTmainly presents a twofold challenge: i) biomechanical design of the wings, and ii) proper control/actuation to module BaTboT's wings.

Prior work in [5] presented experimental results regarding both challenges. The investigation carried out in [5] does not only describes the biomechanical design of BaTboT's wings, but also focuses on evaluating the implications of using SMAs as artificial muscles to power the change of wing's morphology. Figure 14 shows the design-flow process to evaluate key issues of SMA performance and their implications to the application at hand.

The use of SMAs as artificial muscles has been concretely evaluated in terms of two issues:


### *4.2.1. Functionality*

16 Will-be-set-by-IN-TECH

After identification, a low-level PID controller has been designed to address two main limitations of SMAs: slack in the fibers, and limited actuation speed. Slack issues appear when SMA wires develop a two-way memory effect during operation [11]. Limitation in actuation speed occurs due to the large switching time between cooling and heating phases. To address such problems, a pre-heating mechanism has been developed that works in conjunction to the antagonistic arrangement. The pre-heating avoids the temperature on both wires drops below the 10% of the maximum applied electrical current, preventing the inactive alloy from complete cooling. On the other hand, the antagonistic arrangement provides an external stress to the cooling wire (provided both by the elastic backbone and by the active antagonistic wire). Working with an already-warm wire allows for a faster stretch and slack issues are avoided. Note that the PID controller is based on the experimental observation that the hysteresis on the electrical resistance curve was smaller than the hysteresis on the temperature curve. Resistance measurements are used as a feedback signal for closed-loop control (see [59] and

The control developed allows overloading the SMA with up to 350*mA* peak current (note that power signals are sinusoidal, hence overloading only lasts a brief period of time). Overloading has allowed for achieving a 1*Hz* oscillation time (i.e. 0.5 seconds contraction and cooling

A key feature of SMAs is the possibility to develop closed loop control systems without the need of external sensor hardware. The feed back signal is provided by the detection of inner

The main components are described in the following. A micro controller implements the PID algorithm. The PID controller receives the input reference position (set point) and the feedback of SMA's voltage and current that allows calculating the heating current to drive the SMA actuator. The digital output of the PID controller is converted to a reference current in

electrical resistance, that allows an indirect measurement of the temperature.

times) and a bending angle of 36 degrees of each body segment.

=36deg

**Figure 13.** Bending under SMA overloading [59].

*4.1.2. Control architecture*

*4.1.1. SMA control in the iTuna*

[60] form more details).

The SMA actuators shown in Fig. 14 (step-1) are the commercial Migamotor NanoMuscle model RS-70-CE [49]. Each NanoMuscle consists of several short strips of SMA NiTi wire with a thickness of 150*μm* attached to opposite ends of six metal strips stacked in parallel. Each SMA segment pulls the next strip about 0.67*mm* relative to the previous strip, and the relative movements sum to make a stroke of 4*mm*. As depicted, two Migamotors muscles have been arranged into an antagonistic configuration working as artificial biceps and triceps that provide the rotation motion of the wing elbow's joint *θ*3. The range of motion of the joint

18 Will-be-set-by-IN-TECH 70 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

**Figure 14.** Flow-process for SMA evaluation in the BaTboT prototype [5].

is about 60◦. The joint motion is achieved when each SMA actuator contracts upon heating, thus generating a pull-force (*Fsma*). Because both actuators are connected to the joint in an antagonistic fashion, the pull-force *Fsma* generates a joint torque, denoted as *τ*3. Therefore, each actuator requires an input heating power *P*, to produce and output torque *τ*3. The input heating power (*P*) is proportional to the input electrical current (*I*): *P* = *I*2*R*, being *R* the nominal electrical resistance of the NiTi wires, *R* = 8.5Ω.

In [5] simulations and experiments have been carried out aimed at quantifying the Power-to-Force tradeoff of the SMA muscles working under two operation modes: nominal and overloaded. To the application at hand, nominal-mode implies an input heating current (*I*) between 175*mA* and 350*mA*, whereas overloaded-mode, between ~400*mA* and 600*mA*. Overloading allows for increasing the heating-time of the SMA, therefore increasing the contraction speed and the overall actuation frequency. However, overloading must be monitored to avoid overheating issues that may cause physical damage of the shape memory effect. In [5], SMA limitations were found under simulation and validated under experimentation.

Fig.15 shows the Power-to-Force tradeoffs: i) simulation using a SMA phenomenological model, ii) SMA response using an identified model, and iii) experimental measurements of output torque. Herein, our goal is not focused on describing the models, but on comparing the correlations between models (i)-(ii) and experimental data (iii). Further details about the models can be found in [5].

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**step 1. SMA wing actuation**

Migamotor SMA muscles SMA\_1

3 ~ 60º

Elbow Joint

experimentation.

**Bio-inspired insights**

SMA\_2

Antagonistic configuration

P2

**Figure 14.** Flow-process for SMA evaluation in the BaTboT prototype [5].

nominal electrical resistance of the NiTi wires, *R* = 8.5Ω.

P1 F1


is about 60◦. The joint motion is achieved when each SMA actuator contracts upon heating, thus generating a pull-force (*Fsma*). Because both actuators are connected to the joint in an antagonistic fashion, the pull-force *Fsma* generates a joint torque, denoted as *τ*3. Therefore, each actuator requires an input heating power *P*, to produce and output torque *τ*3. The input heating power (*P*) is proportional to the input electrical current (*I*): *P* = *I*2*R*, being *R* the

In [5] simulations and experiments have been carried out aimed at quantifying the Power-to-Force tradeoff of the SMA muscles working under two operation modes: nominal and overloaded. To the application at hand, nominal-mode implies an input heating current (*I*) between 175*mA* and 350*mA*, whereas overloaded-mode, between ~400*mA* and 600*mA*. Overloading allows for increasing the heating-time of the SMA, therefore increasing the contraction speed and the overall actuation frequency. However, overloading must be monitored to avoid overheating issues that may cause physical damage of the shape memory effect. In [5], SMA limitations were found under simulation and validated under

Fig.15 shows the Power-to-Force tradeoffs: i) simulation using a SMA phenomenological model, ii) SMA response using an identified model, and iii) experimental measurements of output torque. Herein, our goal is not focused on describing the models, but on comparing

F2 3 Plagiopatagium skin (0.1mm silicon wing membrane)

> **Re-designing process and adjustments**

R/C transmission link 49MHz

Antenna

motor+ electronics

> SMA morphing muscles

**step 2. Robot assembly**  control encoded.

**step 3. Wind-tunnel measurements.** Implications of SMA performance

**Figure 15.** SMA Power-to-Force response. The input power is of the form: *a* + *b* sin(2*π f t*). a) Simulation of elbow's torque response under nominal and overloaded SMA operation, b) AC small-signal response of SMAs at f=~2Hz, c) maximum peak-values of output torque as a function of the input power

In order to simulate how the SMA muscles response upon electrical heating, a phenomenological model was used. This model is composed by thermo-mechanical equations that describe how the temperature, strain, and stress of the SMA change during its hysteresis loop, going from austenite to martensite and vice versa. Likewise, the SMA phenomenological actuation model is coupled with the dynamics equations that govern the motion of the robot's wing (refer to [5] for further details).

Figure 15a shows simulation results of joint torques achieved by applying nominal and overloaded values of input power of the form: *a* + *b* sin(2*π f t*), where *a* is the mean input power *P*, the term *b* is the small-magnitude of the sinusoidal component, and *f* is the commanded frequency for SMA contraction. Simulation data determines that by applying a nominal input power of *P* = 1.04*W*, the SMAs are able to generate a torque around the elbow joint of *τ*<sup>3</sup> = 0.0007*Nm*, whereas by applying an overloaded input power of *P* = 2.57*W*, the output torque can be increased up to *τ*<sup>3</sup> = 0.0022*Nm*. This implies that by increasing the input power about 2.5 times, the output torque can be increased about three times.

In order to verify the accuracy of simulation results, Fig.15c shows experimental measurements of output torques. In this trial, several profiles of input power were applied, and the respective forces were measured. Note that under nominal-mode, the output torque varies between 0.007 - 0.008*Nm*, whereas under overloading-mode, from 0.016 - 0.018*Nm*. Likewise, at the left side of the plot, the maximum peaks of nominal and overloaded torques corresponding to the simulation in Fig. 15 a, are also shown. One can note there is almost an order of magnitude of difference between simulation and experimental data. The error is produced because the phenomenological model does not take into account the joint friction, and even most important, the anisotropic loading of the silicone-based membrane. However, despite the error in magnitude, note that by doubling the input heating power, the measured

20 Will-be-set-by-IN-TECH 72 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges


**Table 2.** SMA-muscle Power-to-Force performance. <sup>1</sup> Nominal values can be found in Migamotors website [49]. The manufacturer does not provide overloading values. <sup>2</sup> Simulation data corresponds to Fig. 15 a. Please refer to Fig.9 in [5] for details about the SMA phenomenological model. <sup>3</sup> Experimental data corresponds to Fig. 15 c. <sup>3</sup> Identified AC Power-to-force model response. Data corresponding to Fig. 15 b.

output torque increases about 2.5 times. This scaling factor is quite similar compared to the simulation prediction.

The use of a phenomenological SMA model can provide a useful insight into the implications of overheating, by increasing the input power beyond the limits of SMA stress, and thus defining the upper threshold for overloading when using the real system. Unfortunately, the phenomenological model has not proven to be accurate for modeling the response of the SMAs when applying small-signal power inputs. Therefore, the next step is to identify the Power-to-Force AC behavior of the SMA actuators.

As observed by [11], [71] the AC response of NiTi SMA wires behaves as a first order low-pass filter. In [40], [19], [20] similar first-order behavior in their SMA actuator response had also been observed. Therefore in [5], we have followed a similar frequency response analysis procedure for finding a transfer function model that matches the measured gain and phase data of the frequency range of interest. Fig. 16 shows the results.

**Figure 16.** (Experiment VS model) Bode magnitude and phase plots for NiTi 150*μ*m SMA Migamotor actuator. Input heating power of the form: *a* + *b* sin(2*π f t*).

The suitable transfer function that fits the experimental data from Fig. 16 is: *τ*3(*s*) = 0.016(0.35*s* + 1)−1*P*(*s*). The response of the AC model is shown in Fig. 15 b. The AC model is compared against the experimental response of the SMA actuator to the AC small-signal. Note that by applying an input power of ~1.36*W* (I = 400*mA*), the output torque *τ*<sup>3</sup> stabilizes around ~0.008*Nm*. This response corresponds to the real nominal mode of the SMA actuator. Increasing the input power up to ~3.06*W* (overloaded mode, *I* = 600*mA*), the registered output torque stabilizes around ~0.02*Nm*. In both experiments the anisotropic loading of the 0.1*mm* silicone-based membrane has been taken into account.

Note how well the AC model correlates against the real behavior of the SMA muscles. A detailed comparison of the obtained data is summarized in Table 2. In conclusion, to properly evaluate the functionality of using SMA muscles based on the criteria of the application at hand:


### *4.2.2. SMA Performance: actuation speed and fatigue*

20 Will-be-set-by-IN-TECH

**Table 2.** SMA-muscle Power-to-Force performance. <sup>1</sup> Nominal values can be found in Migamotors website [49]. The manufacturer does not provide overloading values. <sup>2</sup> Simulation data corresponds to Fig. 15 a. Please refer to Fig.9 in [5] for details about the SMA phenomenological model. <sup>3</sup> Experimental data corresponds to Fig. 15 c. <sup>3</sup> Identified AC Power-to-force model response. Data corresponding to Fig.

output torque increases about 2.5 times. This scaling factor is quite similar compared to the

The use of a phenomenological SMA model can provide a useful insight into the implications of overheating, by increasing the input power beyond the limits of SMA stress, and thus defining the upper threshold for overloading when using the real system. Unfortunately, the phenomenological model has not proven to be accurate for modeling the response of the SMAs when applying small-signal power inputs. Therefore, the next step is to identify the

As observed by [11], [71] the AC response of NiTi SMA wires behaves as a first order low-pass filter. In [40], [19], [20] similar first-order behavior in their SMA actuator response had also been observed. Therefore in [5], we have followed a similar frequency response analysis procedure for finding a transfer function model that matches the measured gain and phase

**Figure 16.** (Experiment VS model) Bode magnitude and phase plots for NiTi 150*μ*m SMA Migamotor

Nominal

Overloaded

simulation prediction.

Power-to-Force AC behavior of the SMA actuators.

actuator. Input heating power of the form: *a* + *b* sin(2*π f t*).

data of the frequency range of interest. Fig. 16 shows the results.

15 b.

Parameter Theoretical<sup>1</sup> Simulation2 Experimental<sup>3</sup> AC-model<sup>4</sup>

Input power P [W] 0.26 1.04 0.87-1.5 1.36 Input current I [*mA*] 175 350 320-420 400 SMA Pull-force F [*N*] 0.012 0.007 0.07 - 0.08 0.08 Output torque *tau*<sup>3</sup> [Nm] 0.0012 0.0007 0.007 - 0.008 0.008

Input power P [*W*] – 2.57 2 - 2.57 3.06 Input current I [*mA*] – 550 485 - 550 600 SMA Pull-force *F* [*N*] – 0.022 0.16 - 0.18 0.2 Output torque *tau*<sup>3</sup> [*Nm*] – 0.0022 0.016 - 0.018 0.02

> As concluded in [29], [57], [11], [17], [76], PID technique is sufficient for allowing accurate and faster SMA actuation. The key issue for achieving an outstanding SMA performance does not necessarily depend on the control technique, but in complementary mechanisms that monitor the lower and upper limits of input power.

> In [11], and [71], these mechanisms are introduced: i) anti-slack, and ii) anti-overload. The former deals with the two-way shape memory effect [39], improving accuracy and speed,

#### 22 Will-be-set-by-IN-TECH 74 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

whereas the latter limits the amount of input heating power to prevent physical damage when SMAs are overloaded. As a result, the force controller presented in [71] was capable of tracking fast and accurate force references when compared with other works reported in [20], [84].

The improvement in accuracy and speed are due to two factors: i) by avoiding wire entanglement, and ii) by ensuring the passive wire of the antagonistic configuration does not cool completely. Wire entanglement can be produced when the SMA wires extended upon cooling. The passive SMA wire can develop a few millimeters of slack as it cools, which consequently affects the accuracy of the control. This slack-phenomenon is only presented in the antagonistic configuration, due to the two-way shape memory effect produced by each actuator.

To avoid the aforementioned issues, the anti-slack mechanism defines a minimum threshold of input heating power that ensures the inactive wire does not cool completely. The improvement in actuation speed is due to the fact that the already-warm SMA wire can begin to pull as soon as the heating current is raised, whereas a cold wire would first need to be raised to its operating temperature. It has been observed from experimental results in [71] and [5] that a suitable minimum threshold of input heating power is about 10% of the power applied.

On the other hand, the anti-overload mechanism is in charge of ensuring that the maximum input power does not increase above an upper limit. This approach avoids overheating the SMAs in case the controller delivers a large amount of power to the wires. As mentioned before, this upper limit can be found using a phenomenological model, or by performing real measurements of SMA temperature and stress on the wires.

Both anti-slack and anti-overload mechanisms are key for improving on SMA performance under a force control architecture. The advantages of using a force-control scheme are twofold: i) high-bandwidth response, and ii) SMA fatigue avoidance. High-bandwidth response requires the use of force sensors capable of providing the force feedback. It has also been demonstrated in [71], that by using high-bandwidth force feedback, limit cycles of SMA operation are eliminated.

Nevertheless, for some systems, the use of force sensors could be a hardware limitation. In [5], it has been demonstrated that both anti-slack and anti-overload mechanisms can be implemented in a position control scheme. The position feedback can be achieved by measuring the electrical resistance of the SMA wires, which is a linear function of the strain. The key disadvantage of using a position scheme that forces the SMA to behave in overloaded operation mode relies on fatigue. As experimentally observed in [5], overloaded operation mode could be maintained only for about five minutes of SMA continuous operation before decreasing performance to nominal mode. For the application at hand, overloaded mode implied an actuation frequency of 2.5*Hz*, while nominal mode, an actuation frequency of 1.3*Hz*. In this case fatigue issues caused a decrease in actuation speed performance about 56%. Further investigations shall be devoted to quantifying the lifetime of SMAs when subjected to higher stresses and larger heating currents within a position control scheme.
