IEEE Robotics & Automation Magazine - December 2015 - 135

directions with lower RMSE values in all the directions for
Ftd - FtL when compared with Hand 1 with resistance sensing.
Hand 2 is an underactuated hand and does not possess control
over its fingertip contact force directions and is, therefore,
excluded from this measure. Finally, Hand 1 with impedance
sensing has about a third the amount of contact force overshoot when compared with Hand 1 with resistance sensing
across all desired contact force profiles. Hand 2 cannot control
for forces near 1 N or time-varying forces, and was, therefore,
excluded from those tests. However, for Ffinger,max /2, Hand 2
performs reasonably well with an overshoot of 2.864  N.
Undershoot was exhibited with a negative value for Ffinger,max .
To more clearly illustrate the behavior of the force-controlled
system, Figure 18 shows the desired force profile, the contact
force as measured by the intrinsic sensor, and the contact force
as measured by an external load cell for Hand 1, Finger 2 with
resistance sensing. This figure illustrates the complexity surrounding force control of robotic fingers: the sensed forces
closely trace the desired forces (controller error), but the actual
forces are consistently shifted from both the perceived or desired
forces. Since the actual forces are always lower than the perceived forces, the intrinsic sensor appears to have a discrete bias
from its calibration. Furthermore, the large dips in the actual
forces suggest that the contact forces are pushing the intrinsic
sensor beyond its linear response region toward a saturation
limit. This attenuation induces large forces on the load cell as the
intrinsic sensor is now exhibiting nonlinear behavior.

Again, there are three relevant performance metrics for this
test method involving force magnitude, force direction, and
maximum force error. When considering force magnitude,
calculate the RMSE between the tactile sensor force magnitudes (|| FS || ! R) and those measured by the reference force
sensor (|| FL || ! R) for all data collected. When considering
force direction, compute the RMSE between the force direction as measured by the tactile sensor (FtS ! R 3x1) and the external force sensor (FtL ! R 3x1). When considering the
maximum force error, calculate the absolute maximum error
between the contact force magnitude as measured by the hand
sensor and the reference force sensor.

Force Calibration

Figure 18. The desired force profile ^Fd, Z h, the contact force as
sensed by the onboard sensor ^ FS, Z h, and the contact force as
sensed by an external load cell ^FL, Z h for Hand 1, Finger 2 with
resistance sensing.

Metric and Test Method
Force-based sensor calibration is important for
many state-of-the-art robotic grasping and
manipulation control algorithms that use forcebased control approaches. That is, to control
contact forces, force sensor readings must be
accurate. Moreover, force capabilities can be
used for touch-based grasp planning, controlled interaction for texture discrimination
and object localization. This characteristic is a
function of the tactile sensor mechanical
design, and its calibration.
This test method seeks to capture the performance of force-based tactile sensors by comparing the force readings measured by the sensor
^ FS ! R 3x1h to force data recorded simultaneously using an external force sensor
^ FL ! R 3x1h . Using the desired sensor-object
orientation, position the sensor under test just
above the force sensor and verify a zero force
reading. Press the sensor against the load cell
and record both the sensor-force reading and the
load-cell readings. If desired, collect FS during
the finger force tracking test method as well to
extract the necessary information to calculate
force calibration performance metrics.

5

Fd,Z
FS,Z
FL,Z

Contact Force (N)

0

-5

-10

-15

-20

0

10

20

30
Time (s)

40

50

60

Table 6. The force calibration performance errors for two
force-controlled hand layouts.
Robotic Hand

|| Fd | | N

RMSE (N )
|| FL | | - | | FS | | RMSE FtL - FtS

Hand 1 (impedence sensing)

1

1.054

[0.412; 0.529;
0.285]

3.004

Ffinger, max
2

2.855

[0.254; 0.248;
0.118]

7.108

Ffinger,max

2.170

[0.087; 0.154;
0.038]

9.084

Equation 1

2.711

[0.201; 0.257;
0.099]

7.191

1

2.586

[0.218; 0.280;
0.815]

6.380

Ffinger, max
2

4.825

[0.075; 0.427;
0.144]

13.386

Ffinger,max

4.939

[0.062; 0.336;
0.101]

16.398

Equation 1

5.411

[0.093; 0.359;
0.158]

13.003

Hand 1 (resistance sensing)

DECEMBER 2015

*

Maximum
Force Error (N)

IEEE ROBOTICS & AUTOMATION MAGAZINE

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