IEEE Robotics & Automation Magazine - September 2016 - 72

Bolts

Glass Fiber Tiles

Omega Actuator
Flexible Heater
Strain Gauge
Screws

(a)
Strain Gauge

10 mm

Zoomed View

(b)

Figure 6. (a) A modular design of the Robogami self-reconfigurable
surface. Each layer is stacked and attached to one another by
means of screws. (b) The fabricated and assembled module. The
triangular tiles with holes are laser-machined from a lightweight glass
fiber. The strain sensors are sandwiched between two Kapton tapes
of 10-mm width, and four holes are drilled for attaching along with
other layers. Each layer is stacked on top of another and mounted by
M1 screws.

0.9
Measured
Fitted

∆ R (Ω)

0.7
0.5
0.3

∆R = −0.0053θ + 0.83

90
Angle (°)

120

150

Figure 7. The curvature sensor resistance change for the angular
deflection of the actuator upon activation. The sensor displays
minimal effect of the heat dissipating from the microheater layer.

the degrees of freedom (DoF) by mounting additional modules or dismounting them using two pairs of M1 screws.
We adopt commercial strain gauges (RS Components
Ltd.) for curvature angle measurement, as depicted in Figure 6. The sensor undergoes relatively high resistance changes for bending strains. Since the actuator has one-way
deflection, the sensor layer here acts as a bias element to partially reverse the actuator motion during cooling. Thus, the
sensor is sandwiched between 50-μm-thick Kapton tapes to
improve the stiffness and the thermal insulation. Characterization test results provided in Figure 7 show an approximately linear resistance change of the sensor for the angular
72

IEEE ROBOTICS & AUTOMATION MAGAZINE

The Controller Design
There are generally two control goals for SMA actuators: position and force. Control parameters can be resistance, temperature, position, or force feedback. Our application focuses on
the Robogami system with multiple creases that can self-fold
into different 3-D shapes. Therefore, accurate position control
of the actuators is essential for achieving the versatile shapes.
We present here an angular position control of the X-SMA
torsional actuator by PWM duty modulation of the power
input. Since we are interested only in accurate positioning of
the actuator, we designed our controller based on angle feedback from the bending strain sensors described earlier. Different from our previous work on an on-off controller of SMA
actuators [18], here a proportional-integral (PI) controller is
adopted to achieve the desired positions for each actuator.
The controller design is as follows: if a closing hinge with
a measurable bending angle i is considered, then the control
goal within the PI controller framework can be written as
D = K p (i set - i) + K i

0.1
−0.1

deflection of the actuator upon activation. Here, an experiment similar to the load-free test is carried out-with the
sensor mounted across the actuator hinge, as shown in
Figure 6-and the actuator is characterized in a single direction from the open configuration to the closed. The deflection angle is captured using a video camera, where the
resistance value is measured using a digital multimeter (an NI
USB-4065, National Instruments) interfaced with LabVIEW
software (National Instruments). It is worth mentioning that
due to the elasticity of the sensor layer, it adheres to the
curved shape of the actuator and heater hinge after multiple
bending cycles, as shown in Figure 6(b). However, there is no
contact between the sensor and heater layers; therefore, the
heat effect on the strain sensor is minimal.

September 2016

# (i set - i) ,

(7)

where D is the PWM duty value of the power supplied to the
heater and K p and K i are the proportional and integral gain
constants to minimize the error in the bending angle, which is
the difference between the set angle i set and the measured
angle i coming from the strain sensor. To avoid overheating
of the actuator, we introduced limiting functions for the
controller duty value output as
D ='

D lim
0

if D 2 D lim
,
if D 1 0

where the limiting duty value is a positive real number:
0 # D lim # 1.
Implementation and Results
To evaluate the effectiveness of the method, the setup given
in Figure 8 is employed to test a Robogami surface with
four tiles, illustrated in Figure 9. It consists of three actuated
modules to demonstrate the capability of constructing various shapes in 3-D space by the selective activation of three
actuators and controlling the folding angles. The setup is as

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2016