IEEE Robotics & Automation Magazine - December 2015 - 134

force control stability issues that can occur near singular configurations. During the test, the desired force profile (Fd ! R 3x1) and
the contact forces measured by the load cell (FL ! R 3x1) are all
recorded for extracting performance measures.
There are three relevant performance metrics for the test
method involving force magnitude, force direction, and force
Six-Axis
Load Cell

(a)

(b)

Figure 17. Test setup for finger force tracking. A nonlinear admittance
control algorithm was implemented on Hand 1 with (a) resistance
sensing, and (b) impedance sensing to achieve force tracking
capability. (Images courtesy of NIST.)

Table 5. The force-tracking performance errors
for three force-controlled hand layouts.
Robotic Hand

|| Fd | | N

Hand 1 (impedence sensing)

1

0.567

[0.124; 0.428;
0.323]

1.046

Ffinger, max
2

2.182

[0.020; 0.225;
0.102]

4.972

Ffinger,max

1.773

[0.015; 0.134;
0.021]

5.159

Equation 1

2.092

[0.024; 0.204;
0.082]

5.160

1

2.121

[0.218; 0.285;
0.483]

6.382

Ffinger, max
2

4.577

[0.075; 0.398;
0.178]

12.028

Ffinger,max

4.032

[0.062; 0.283;
0.133]

16.746

Equation 1

5.013

[0.093; 0.330;
0.223]

14.223

1

N/A

N/A

N/A

Ffinger, max
2

1.226

N/A

2.864

Ffinger,max

5.129

N/A

-3.012*

Equation 1

N/A

N/A

Hand 2 (current
sensing)

* Indicates system undershoot.

*

Experiments
Each robotic finger was commanded to impart a certain contact
force magnitude and direction on a six-axis load cell, as shown in
Figure 17. A nonlinear admittance control algorithm was implemented on Hand 1 to yield force tracking, while only the stock
force control capabilities were used on Hand 2. Specifically, a contact force magnitude of 1, Ffinger,max /2, and Ffinger,max were commanded where Ffinger,max is based on the maximum end-effector
force capability as measured in the "Metric and Test Method"
section (Ffinger,max is 10 N for Hand 1 and 30 N for Hand 2).
These values were chosen to investigate force-tracking capabilities at extrema (and approximately their average) to reduce the
performance search space. A time-varying force
profile was also issued for those fingers with
force-tracking capabilities and is defined by

RMSE (N )
|| Fd | | - | | FL | | RMSE Ftd - FtL

Hand 1 (resistance sensing)

134

peak overshoot. When considering force magnitude, calculate
the root mean squared error (RMSE) between the desired
force magnitude ^|| Fd || ! R h and for the forces measured by
the reference force sensor ^|| FL || ! R h . When considering
force direction, calculate the RMSE between the desired force
magnitude (Ftd ! R 3x1) and for the forces measured by the
reference force sensor (FtL ! R 3x1). When considering peak
overshoot, calculate the peak overshoot (Fpeak ! R) between
|| Fd || and || FL ||.

IEEE ROBOTICS & AUTOMATION MAGAZINE

*

DECEMBER 2015

Force Peak
Overshoot (N )

N/A

|| Fd, z || = 5 log c sin c

r (t + 3)

2

m

+ cos ` t + r j + 3 j + 1,
4
(1)

where t ! R is time and Fd, z ! R is the
desired force trajectory in the world coordinate system's z-axis. This spread of force magnitudes was chosen to test the hand's abilities
to follow set-point force tracking for small,
medium, and large forces that scale with the
capabilities of the hand. The time-varying
force profile contains multiple frequencies
and a range of magnitude shifts to more thoroughly test the force-tracking performance.
All measures were obtained by recording
force-tracking data for 60 s of continuous
control operation for each finger, and averaged over all fingers per hand layout.
Table 5 shows the results obtained for the
controller's actual performance. In particular,
the results show that Hand 1 with impedance
sensing yields the RMSE values for
|| Fd ||-|| FL || of at least half those obtained
for Hand 1 with resistance sensing. Hand 2
performs similarly to Hand 1 when
|| Fd || = Ffinger,max /2, but generates much
larger RMSE values over 5 N at Ffinger,max . In
general, Hand 1 with impedance sensing
allows for improved control over contact force
Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2015
