IEEE Robotics & Automation Magazine - December 2022 - 88

(8) and (9). These optimization problems reflect the need to
select the optimal detachment of feathers to increase the thrust
in one direction or to maximize the controllability of the structure,
respectively. In particular, we provide an example of starting
in a horizontal configuration and moving in the vertical
direction. For this case, we consider solving the two different
optimization problems and assess how the solutions lead to
changes in controllability or speed. In option 1, we apply the
optimization problem described in (9). We are therefore maximizing
the possibility to control the structure, with the resulting
structure able to move linearly, as shown in Figure 10(a), and to
turn, as shown in Figure 10(b). However, this possibility in control
comes at the cost of lower acceleration in both motions.
On the other hand, in option 2, we apply (8), with the
parameters of the cost function being [, ,]kk k
[ ,,].111 We are therefore maximizing the total thrust
Ttotrollpitchxx =
-produced
by the structure while penalizing any turning
motion. For this optimization problem, the solution is to
detach the asymmetric feather so that, when actuated,
both layers will produce thrust in the same direction.
0.005
0.01
0.015
0.02
Feather 1
(a)
T = 25 s
Feather 2
These results are reflected in Figure 10(c). These results
show that with option 2, a speed increase of over 60% can
be achieved with the optimal feather detachment. Thanks
to (8) and (9), we are therefore able to intuitively specify
the desired behavior of the robot by tuning few parameters
in the cost function of the optimization problem, and the
optimal feather detachment will be computed, considering
the internal dynamics of the system described in (7).
Discussion and Conclusion
Biology provides many examples of mechanisms by which
adaptation of the body can be used to simplify complex
functions or enable otherwise impossible functionality.
The feather star provides a number of fascinating examples.
Using this as an inspiration, we have developed a
robot with feathers that utilizes these passive structures
for swimming and the detachment of the feathers to
change its structure. Utilizing modeling and experimental
results, we have optimized the morphology and control of
these feathers and developed a theoretical framework
Controller 3
Controller 2
Controller 1
Feather 1:
L:120 W:40
T = 25 s
Feather 2:
L:192 W:25
Controller 1
R:0.1 F:0.5 H:0
Controller 2
R:0.1 F:1 H:1
(b)
Figure 8. A comparison of the optimal feathers (120 × 40) and baseline with the same area (192 × 25) for three different controllers.
Each experiment was repeated five times, with the velocity and standard deviation presented.
88 * IEEE ROBOTICS & AUTOMATION MAGAZINE * DECEMBER 2022
Controller 3
R:0.5 F:0.5 H:1
Velocity (m/s)

IEEE Robotics & Automation Magazine - December 2022

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