# Compensating Uncertainties in Force Sensing for Robotic-Assisted Palpation
## 4 Experiment Studies and Result Analysis
### Uncertainties of Force Measurement  
To deal with the uncertainties exist in the force sensor measurement, free motion experiments are performed, the free motion experiments mean that the robot is moving along the \(Z\) axis but without contacting any objects, in which the probe does not contact any object, and the robot is moving while performing the palpation task along the \(Z\) axis. The experiment setup is shown in Figure 6. Since the probe is not influenced by any contact force, the force sensor is supposed to only contain the inertial force and unavoidable noise, the expected mean of the noise is supposed to be 0.0 N in the experiments. The effect of gravity of the probe is compensated by the initialization of the force sensor before the robot starts to move. Two different experiments are conducted to move the robot 15 times, and the force read from the sensor are recorded and analyzed as shown in Figure 7. It is noticed that even without contacting any object and with no probe attached on the sensor, a noticeable force (average force is \(-0.0874\) N) is obtained from the sensor due to the noise and other force measurement uncertainties. When the probe is attached to the sensor, an even larger force is provided from the sensor (average force is \(-0.1929\) N). These experimental results show that force measurement uncertainties exist during the robotic palpation task; when a probe is attached to the sensor, significant force measurement uncertainty is caused, which may further deviate the force measurement. Figure 8 shows the force response of 10 times that of free motion experiments with the probe attached on the force sensor, which needs to be compensated to get accurate force measurements. From Optoforce sensor datasheet, it is mentioned that the sensor measurement range is 200 N, and the resolution (typical) is 133.33 mN, but all with static measurement considering sensor movement and the object attached on the sensor.  
Figure 5: Experiment Setup with UR5 robot and silicone based soft tissue phantom with hard inclusions. \(Optoforce\) sensor is attached to the robot end effector to measure the contact force during the palpation. Three hard inclusions which are stiffer than the soft tissue phantom are embedded at different depths (depth here denote the distance between the place of hard inclusions and the surface of the tissue phantom): 5 mm, 8 mm, 10 mm.  
Figure 8: Force data from the force sensor with 10 free motion experiments (with probe attached on the force sensor). During the experiments, the probe does not contact any environment. Each experiment is conducted for around 80 s. Noticeable force is observed and recorded as shown in the figures.  
Figure 6: Force uncertainty experiment setup. Experiment A: The probe is not attached on the sensor. Experiment B: A 3D printed probe is attached on the sensor. The experiments are performed by moving the robot in the \(Z\) axis with moving up 2 cm and down 2 cm 10 times, which last for around 80 s.  
Figure 7: Force uncertainty experiment result analysis. All of the force information is recorded and analyzed for experiment A and B. Significant force uncertainty can be observed in experiment B, where the probe is attached on the sensor. The unit for the force is \(N\).