Comparison of IBVS and PBVS regarding robustness towards sensor noise

robustness towards sensor noise on the basis of

simulations

The following section will highlight the capabilities of both, IBVS and PBVS in dealing with sensor noise. For reasons of repeatability and simplicity the comparison will be conducted in simulation. As for the robotic platform, Air-Cobot, both techniques are used depending on which is the more effective one. Through empirical studies we have found the optimal techniques for each visual servoing target. However as a rule of thumb, so to say, IBVS tends to be much faster and better if the target can be well identified and tracked. PBVS on the other hand tends to work better with more challenging targets since it allows to track them even in difficult conditions since the pose estimated can be continued with odometry or other means of localization whenever the target is occluded. In order to allow a thorough analysis we have decided to use simulations to compare both techniques. This decision enables us to control the amount and distribution of noise. Although the lab environment is already much more controllable than tests in an aircraft hangar or experiments on the airport tarmac, it is still possible that the initial conditions will not be the same for every experiment. During our tests in the G´erard Bauzil at LAAS-CNRS room we have found that experimental results differ depending on the time of day and even the season of the year. Since the room is equipped with very large windows the luminosity is not constant.

The following sections will explain the simulation conditions that were chosen for the comparison.

3.5.1. Simulation conditions

A white Gaussian noise is added on the image plane coordinates with a 2 % magnitude, for each point in the camera image Pi = (Xi, Yi)T, a noisy one ˆPi = ( ˆXi, ˆYi)T where :

ˆ

X = X (0.99 + 2 rand(0.01)) with

= X ± 1

(3.36)

To add noise to the simulation we make use of the MATLAB AWGN function. This function includes an ”Additive white Gaussian noise” to the simulated camera signal, thus altering the position at which the feature detection would suspect the target. Op- pose to general probability terminology the SNR (Signal to Noise Ratio) factor deter- mines the amount and therefore the amplitude of the applied noise. Adding noise is important to determine the quality and robustness of our results. Since a simulation can provide the controlled environment we are looking for adding Gaussian white noise allows us to capture some of the properties of real life experiments.

−4000 −2000 0 2000 −1500 −1000 −500 0 500 600 650 700 750 800 X_RW Path of C in RW Y_RW ZR W point C xCamera yCamera zCamera

(a) IBVS: signal to noise ratio = 45

−4000 −2000 0 2000 −1500 −1000 −500 0 500 600 650 700 750 800 X_RW Path of C in RW Y_RW ZR W point C xCamera yCamera zCamera

(b) PBVS: signal to noise ratio = 10

Figure 3.16.: Evolution the point C (camera origin) in a noisy simulation

3.5.2. The obtained results

Table 3.3 gives the initial and the desired pose of the robot. As can be seen the camera sensor is placed about 3 meters from its desired goal. In our experiments we determine the desired feature vector, s∗_{, by virtually placing the sensor at the desired position and} taking a snapshot. The displacement on the y − axis simply allows to eliminate the possibility of sign errors in the robot Jacobian.

XM[mm] YM[mm] θ[rad] θp[rad] θt[rad]

Desired pose −500 −900 0.0 0.0 0.0

Initial pose −3500 −900 − π

180

π

180 0.0

Final pose (IBVS) −451.67 −905.31 −0.1127 −0.1672 ∼ 0 Final pose (PBVS) −478.54 −905.52 −0.3240 −0.3239 −0.0022

Table 3.3.: Parameters of the IBVS/PBVS comparison

Figure 3.16 displays the movement of the camera in the world frame. During the ∼ 2 meter displacement in this mission there is hardly a difference to recognize which is to be expected since the targeted configuration can be reached almost with a straight line. The second figure relevant in this discussion shows the evolution of the features in the image plane. It basically displays an image that was build from the position of the four features for each cycle of the simulation. Figure 3.17 highlights the difference in the signal to noise ration used for IBVS and PBVS. In Figure 3.17(a) we can observe that the evolution to each feature resembles almost a straight line (blue), where else the features for PBVS (SNR = 10) are much more spread throughout the image plane. Therefore, it is remarkable that PBVS still manages to converge. The most likely reason for that is that the methods input is not any of these features, but however an average

3. Multi Visual Servoing −1.2 −1.1 −1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 x in image plane y in image plane

Evolution of features in image plane Target points desired (noise) Target points initialization (noise) Target points desired (gt) Target points initialization (gt)

(a) IBVS: signal to noise ratio = 45

−3 −2.5 −2 −1.5 −1 −0.5 0 0.5 −0.1 −0.05 0 0.05 0.1 0.15 x in image plane y in image plane

Evolution of features in image plane Target points desired (noise) Target points initialization (noise) Target points desired (gt) Target points initialization (gt)

(b) PBVS: signal to noise ratio = 10

Figure 3.17.: Evolution of features in a noisy simulation of all four. Hence, the Gaussian distributed noise is reduced.

A third figure monitoring the successive position and orientation of the robot and the camera angles furthermore underlines that there is a difference to IBVS and PBVS. However, keeping the scale of the diagrams in mind, Figure 3.18 shows that this difference is rather small and can also attributed to the different noise ratio for a small part.

To complete the survey two last figures are presented. Figure 3.19 gives insight to the system’s error and Figure 3.20 to provide a view of the robot velocity differences. It is obvious that for IBVS in Figure 3.19(a) the noise ration never becomes a major factor. Only towards the end of the simulation the error actually seems to spike. For PBVS (Figure 3.19(b)) however, the noise determines the rate of convergence quite early (iteration ∼ 2000). As to be expected, the velocities shown in Figure 3.20 are quite similar.

The outcome of these experiments show that PBVS can be more robust if the neces- sary computational power can be provided and the target consists of many redundant features. IBVS on the other hand is a fairly straight forward approach that does not need a pose estimation (depth estimation), but can profit of it. As stated before, on the Air-Cobot platform both techniques are used, depending on which features are currently recognized (the rest of the aircraft features are estimated with the help of an 3d model of the A320). The following section will provide these real life experiments.