IEEE Robotics & Automation Magazine - December 2022 - 83

replicates the simulation. It uses a servo-powered mechanism
to actuate the base of the feather, with a load cell used
to measure the upward thrust. The setup ensures that there
are no moments applied at the load cell so that it truly measures
the upward thrust. Figure 5 shows the thrust measurements
for the subset of parameters selected from the
simulation results. Here, we observe the extreme sensitivity
of the generated thrust for different design parameters.
This highlights the complexity of optimizing the parameterized
feather, even after reducing the design space to five
parameters, and a need to use simulation to systematically
explore and reduce the design space while not missing local
maxima. From these results, some conclusions can be
drawn to identify the optimal parameters
p .des
*
For the geometry, we identify the parameters [, ]wl =
[, ] as optimum, as they have the highest thrust
40 120
recorded and the highest average thrust across different
controllers. For the controller, for the optimized
feather ([ ,] [, ])
rise
des = 40 120 01 05 0
The black bar graph in Figure 5 shows
the performance of the poorly performing
controller in simulation. We
observe that this controller is consistently
poorly performing for all feather
sizes, which corresponds to the
simulation results. Going forward, we
refer to the optimal motion parameters
([ ,, ][ ., ., ])
tt tfall hold = 01 05 0
rise
rise
fall hold
[. ,,])
as
controller 1, to the second-best
motion parameters ([ ,, ]tt t
=
0 111 as controller 2, and to the
poorly performing parameters as controller
3.
Computational Design of the
Robot Structure
For the specific structure of the robot,
we consider a two-layered system,
where each layer has six feathers that are
attached to the body radially and symmetrically
(Figure 6). Therefore, in this
specific design, we used n = 6 and
.
n 2s
=
Each layer of feathers can be
actuated collectively, with the angle of
the base of each feather controlled in
the same way as in the simulation and
experimental validation. Due to the
sensitivity of the thrust generation of
a feather to slight changes in the controller
(Figure 5), maneuverability
through the control of individual
feathers would be ineffective. Thus,
control of the motion must be
achieved with a constant controller
Motion
Arduinos
p .des
Reaction Force
Figure 4. The experimental setup for isolating and measuring the thrust generated by
feathers of different values of
2.5
2
1.5
1
0.5
w: 25
l: 120
w: 25
l: 140
w: 32.5
l: 130
R:0.1 F:0.5 H:0
R:0.1 F:0.5 H:0.5
R:0.1 F:0.5 H:1
R:0.1 F:1 H:0
w: 40
l: 120
R:0.1 F:1 H:0.5
R:0.1 F:1 H:1
R:0.5 F:0.5 H:1
Figure 5. The experimental thrust values for a subset of feather geometries and
controllers identified from simulation.
DECEMBER 2022 * IEEE ROBOTICS & AUTOMATION MAGAZINE *
83
w: 40
l: 140
Controller 3
qc ,
i,ji,j
wl = 40 120 we identify the parameters
)
= tvj
[, ,]tt tfall hold =[. ,. ,]01 05 0 as optimum. Hence, we have
identified p [, , ., ., ].
and by utilizing changes in the body. In this section, we
define how the desired change in behavior can be achieved
by varying the morphology of the structure, i.e., by detaching
feathers. To this end, by analyzing the controllability of
the robot, we can then develop algorithms for the optimal
detachment of the feathers, aimed at increasing the directional
acceleration or restoring the maximal maneuverability
of the design.
Since the feathers are actuated in synchrony, we can write
the position q Rn
c =ij,
01
motor position v ! R .ns
! of the n feathers as a function of the
We can define the configuration of
the robot with a configuration matrix C Bnns# , with
{, }. A value of one represents the presence of a feath!
er
in the ith position for the jth motor, while a value of zero
represents a detached feather. Consequently, it holds that
(3)
where ρ is the transmission ratio between the feather and
motor coordinates. To identify designs that are able to
maneuver with the minimal number of actuators, we first
Single Feather Test Setup
Encoder
T = Fry
Servo
Single
Feather
Fry
Frx
Load
Cell
Controller 1
Controller 2
Thrust, T (mN)
IEEE Robotics & Automation Magazine - December 2022

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