IEEE Robotics & Automation Magazine - June 2020 - 72

the optimal parameter values would be, so these ranges are
the broadest that were reasonable for the problem; other network and learning hyperparameters could be considered, but
this set of 10 seemed reasonable based on past experience
with deep learning using this sensor.
Tactile Pose Estimation for a 3D Surface
3D Surface Model Results
The performance of the trained PoseNet was assessed on
a third test data set gathered for this purpose, consisting
of 2,000 tactile images labeled with depth, roll, and pitch
pose parameters. The data were subject to random

Table 2. The search ranges used to optimize the
PoseNet hyperparameters.
Parameter

Range

Distribution

Number of convolutional
hidden layers, N conv

{1, 2, 3, 4, 5}

Uniform

Number of convolutional
filters, N filters

{2, 4, 8, f, 512}

Uniform

Number of dense hidden
layers, N dense

{1, 2, 3, 4, 5}

Uniform

Number of dense hidden
layer units, N unit

{2, 4, 8, f, 512}

Uniform

Hidden-layer activation
function

{ReLU, ELU}

Uniform

L1-regularization coefficient

[10 -4, 10 -1]

Log uniform

L2-regularization coefficient

[10 -4, 10 -1]

Log uniform

Dropout coefficient

[0, 0.5]

Uniform

Batch size

{16, 32, 64, 128} Uniform

Analysis of 3D Surface Model Optimization
The benefit of optimizing the hyperparameters is evident
from the 1,000-fold decrease in the validation loss
through the 300 trials of training [Figure 8(a)]. The first
50 trials featured a period of high scattered loss during
the startup evaluations (0.05 K MSE K 2). Then, within
another 20 trials, the optimizer quickly found a good
model (MSE - 0.01). Another 150 trials were needed
before the optimizer improved substantially to give
the best loss (MSE - 0.005), by which time it consistently gave models with low losses. The convergence of
the optimization process can also be seen by plotting
the hyperparameters against their corresponding losses, visualized as scatter plots ordered by the loss (Figure 8). As the loss becomes small (to the left), the

15

-1
MAE = 0.1 mm

15
MAE = 0.3°

MAE = 0.3°

10

-3

-4

10
Predicted Pitch, θny (°)

-2

Predicted Roll, θnx (°)

Predicted Vertical, tz (mm)

unlabeled perturbations in the target pose prior to collecting the tactile image, using the procedure described
in the "Training Data Collection" section. All labeled
poses and unlabeled perturbations were sampled randomly within the same ranges as the training and validation data (Table 1).
Highly accurate performance was obtained for the optimized PoseNet, with a close match between the predicted and
labeled pose parameters (Figure 7). The mean average error
(MAE) between predictions and labels was used to summarize the model performance, giving values of 0.1 mm for the
depth and 0.3º for the roll and pitch. These results are precise
compared with the size of the tactile sensor (40-mm diameter
tip) and pin spacing (4 mm); also, the TacTip was not
designed for this task but was a standard version used in our
lab [24]. We emphasize that the precise accuracies hold even
though the data were randomly perturbed by an unknown
shearing motion that significantly affected the tactile
image (Figure 6).

5
0
-5
-10

-5
-5

-4
-3
-2
Vertical, tz (mm)

-1

(a)

-15
-15 -10

5
0
-5
-10

-5

0

5

10

15

-15
-15 -10

-5

0

5

Roll, θnx (°)

Pitch, θnx (°)

(b)

(c)

10

15

Figure 7. The optimal PoseNet performance for the 3D surface, with the predicted (a) vertical, (b) roll, and (c) pitch results. The
smoothed predictions (red: 100-sample moving average), region within the smoothed absolute error (pink), and MAEs are shown.

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IEEE Robotics & Automation Magazine - June 2020

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