Biomedical Engineering Reference

In-Depth Information

multiplied to
R
T
E
. However, computation of this rotation matrix can be integrated

easily into the above described system of linear equations.

5.1.2 Gravity Compensation and Tool Calibration

With the FT sensor calibrated to the robot's end effector, we are now able to detect

impacts (measured as forces and torques) on the mounted tool in robot coordinates.

However, due to gravity, the tool's weight affects the sensor and consequently the

force/torque measurements.

To measure and detect these impacts with the sensor, e.g., user interaction or a

collision, we have to compensate for the tool's weight. By changing spatial ori-

entation of tool and sensor, the influence of the weight on the recordings changes.

Hence, we need to consider the gravity force depending on the current robot end

effector orientation
R
T
E
. Therefore, we have to apply the transform
E
T
FT
from the

robot's end effector to the sensor, accordingly.

Any tool mounted to the FT sensor has its specific tool parameters. Its gravity

force f
g
depends on the tool's mass (weight) m and the gravity acceleration

g
¼
9
:
81 m/s
2
. The gravity force can be calculated as:

f
g
¼
m
g
:

ð
5
:
9
Þ

Furthermore, the tool consists of a specific centroid
s which is the center of

gravity. At
s the gravity force acts and results in torques M
G
, as presented in

Eq. (
5.1
). However,
s is not purely tool specific. As
s is represented in the FT

sensor's coordinate frame, i.e. with respect to the origin of the FT sensor, the way

the tool is mounted is important, too. Thus,
s changes with re-mounting, whereas f
g

stays constant.

For any tool (re-)mounted to the FT sensor we must therefore estimate f
g
and
s.

With a known end effector orientation, we are then able to subtract the gravity part

on the force and torque measurements for that orientation. In this way, we can use

the gravity compensated forces and torques to record impacts on the tool.

To calculate the tool parameters, again we use a set of n initial measurements

(F
i
;
M
i
).

To

calculate

the

gravity

force,

we

apply

Eq. (
5.6
)

and

average

it

throughout the recordings:

X

n

2
:

f
g
¼
1

n

F
i

ð
5
:
10
Þ

i
¼
1

Subsequently, we use Eq. (
5.1
) with the recorded measurements to compute the

centroid
s:

M
i
¼
F
i
s
;

8
i
2½
1
;
n
;

ð
5
:
11
Þ

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