IEEE Robotics & Automation Magazine - September 2023 - 54

as it reacts only to velocity and cornering stiffness,
with a damping coefficient of
p 1 .= In
"
contrast, the neural gain method is able to fluctuate
the damping coefficient by modulating
both Kp and Kd independently. This enables
the technique to increase p when the set point
is reached in the " Init " section
^hs 20 m.
.
BECAUSE NEURAL
NETWORKS ARE
The process keeps p low in the corners and in
straight lines to follow the trajectory closely,
and the procedure increases p when perturbations
occur and when the curvature changes
quickly. This modulation of damping coefficient
p allows the neural gain scheme to
increase the reaction to follow the trajectory closely when it is
safe, while reducing the reaction when an oscillatory behavior
is possible.
NEURAL GAIN ANALYSIS
Because neural networks are black boxes, they are notoriously
hard to analyze. However, there exists an analysis that
assesses which inputs are considered important for neural
networks, called feature importance. Feature importance
represents the percentage of contribution of the output's fluctuation
with respect to each input's expected range, determined
from representative experiments [19]. As an example,
from Figure 10, the 24% feature importance of Kp for the
robot's xR, yR position accuracy (Cxy) implies that Cxy contributes,
on average, to 24% of the fluctuation of Kp. This is
determined empirically using a temporal shuffling methodology
[19].
From Figure 10, the most important inputs for gain predictions
(contributing 10% or more) are (in order) the target speed
,
robot's
vtarget rate of change of angular deviation (/ ),ddtiu
xR, yR position accuracy Cxy, future curvature 6future cs ( ),@
velocity v, and cornering stiffnesses CF and CR.
These results show a concordance with the deterministic
gain method as CR, CF, and v are considered important.
However, it also shows that gains for the neural gain scheme
BLACK BOXES, THEY
ARE NOTORIOUSLY
HARD TO ANALYZE.
„
are more affected by the target speed, rate of
change of angular deviation, accuracy in position,
future curvature, and lateral error. This
is understandable, as each one affects how
the system responds or how it will respond to
tracking errors, and as such, using them in a
gain tuning method will lead to a more complete
gain prediction practice.
Furthermore, some key insights are visible
from Figure 10. If speed v and target speed
vtarget are ignored, the next most important feature
for the Kp gain is Cxy, Kd gain is (/ ),ddtiu
and prediction horizon H is Cxy and future c(s).
This means that the Kp gain mainly reacts to position accuracy
to avoid reacting to noise, which, when minimizing the
errors, the Kd gain mainly reacts to (/ )ddtiu

IEEE Robotics & Automation Magazine - September 2023

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