4.2. Parameter Settings for Experiments
The parameter settings in the experiments are shown in
Table 1. In this paper, we employ the SIFT features of the image as landmarks. On the premise of accurate results, we modified several parameters recommended by Lowe in [
31] to get more SIFT features. Firstly, the number of scale layers
S where SIFT features are extracted is increased from 3 to 5, which can both increase the total number of extracted landmarks and maintain a reasonable time of execution. Secondly, the response threshold of extreme points
TDOG in the difference of Gaussian images is decreased from 0.08/
S to 0.04/
S in order to get more features from areas of low contrast, as indoor environments often contain such areas.
Table 1.
Parameters for the experiments.
Table 1.
Parameters for the experiments.
Parameters | Value | Parameters | Value |
---|
S | 5 | αW | [0, 355]/72/5 |
TDOG | 0.04/S | nR | 5 |
ρW | [0, 0.95]/20/0.05 | VTH | 4 |
ψW | [0, 355]/72/5 | | |
In
Table 1, the parameter format of
ρW,
ψW and
αW is shown as search range/search steps/resolution. In order to give full play to the performance of the warping method in the experiments, we adopted the parameters recommended by Möller in [
30]. The search range of
ρW is [0, 0.95], and there are 20 search steps. The settings of
ψW and
αW are the same, whose search range is [0, 355], and there are 72 search steps. In addition, according to the requirements of the proposed homing algorithm, the number of the reference landmark pairs
nR and the threshold
VTH for eliminating the mismatching landmarks were separately set to 5 and 4.
We separately took 100 pairs of images from the three image databases randomly. These image pairs were used as the goal image and the current image. Based on the parameter settings in
Table 1, we determined the average computation time for two methods (2 GHz Pentium (R), MATLAB R2007b), as shown in
Table 2. It can be seen that the average computation time of the warping method for each homing test was about 40% more than that of our method. We consider the settings in
Table 1 reasonable enough for the comparison of homing performance.
Table 2.
Average computation time for the two methods.
Table 2.
Average computation time for the two methods.
Method | Average Computation Time (s) |
---|
original | arboreal | day |
---|
Warping | 21.051 | 18.643 | 19.541 |
Proposed | 14.559 | 12.638 | 13.854 |
4.3. Performance Metrics
According to the previous presentation, the goal position and the current position are denoted separately by H and C in the experiments. In this paper, three metrics known as angular error (AE), average homeward component (AHC) and return ratio (RR) are adopted to evaluate the performance of the proposed method.
For a pair of H and C, suppose the homing angle computed by the homing algorithm is indicated by
βhoming.
βideal represents the ideal homing angle, which directly points from C to H. The angular error can be determined as:
where the function of
diff() refers to Equation (6).
The average homeward component, used in the homing experiments frequently, is the evaluation criterion, which can measure both the validity and the angular deviation of the computed homing angles. As long as the value of AHC always stays above zero, the robot travels nearer to the goal position; the closer the value of AHC is to 1, the closer the movement direction of the robot gets to the ideal homing direction. Based on the angular error, the average homeward component can be defined as follows:
where
n indicates the number of different pairs (H, C) selected in the experiment scene. In the experiments of AHC, we separately took 100 pairs of images from the image databases randomly according to the distance between C and H, which ranges from 30 to 390 cm in steps of 30 cm.
The last performance metric is the return ratio [
18,
19], which is defined as the successful percentage of homing trials. The return ratio can be computed by carrying out simulated homing trials on the capture grid of the image databases. A dummy robot is placed at all integer grid positions and allowed to move according to the homing vectors, which have been pre-computed with the two methods. The robot moves at a step of
rh, which is generally determined by the ratio between the actual step length of the robot and the sampling interval of the images. The value of
rh was set to 0.8 in the trials.
βh(
x,
y) denotes the homing angle pre-computed at each position in the capture grid, and the motion direction of the robot is determined by
βh(
x,
y), whose position is closest to the current position. A trial is considered successful if the robot can reach a place within a given distance threshold of H from C. The threshold was set to 0.5. The result of a homing trial at position C can be evaluated as follows:
Step 1: The robot moves a step according to the corresponding βh(x,y).
Step 2: If the following two cases happen, jump to Step 4.
Step 3: Continue to perform Step 1.
Step 4: If Case 1 happens, the homing trial is successful; if Case 1 does not happen and Case 2 happens, the trial has failed.
We define
λ(H,C) as a binary evaluation function with a value of 1 for successful homing and 0 for unsuccessful homing. The return ratio is determined as:
where
n indicates the number of different current positions selected in the experiment scene.
4.4. Homing Experiments on Image Databases
The image databases introduced in
Section 4.1 were used to perform the experiments. The experiment environment of the scene in this section was divided into two classes: (1) static environment: the surroundings of the scene remain static during the experiment; (2) dynamic environment: the objects or illumination in the scene changes during the experiment. According to different experiment environments, three different groups of experiments were conducted: (1) Group 1: the main goal is to test the homing performance of the proposed method under static conditions; both current images and goal images were selected from the database original, and this experiment condition was represented by original-original; (2) Group 2: the main goal is to test the homing performance of the proposed method when the objects in the scene change; the changing of objects was simulated by using cross-database experiments,
i.e., the current images were taken from the database original, and the goal images were taken from the database arboreal; the experiment condition was represented by original-arboreal; (3) Group 3: the main goal is to test the homing performance of the proposed method when the illumination of the scene changes; similar to the second group of experiments, the current images were taken from the database original and the goal images were taken from the database day, in order to simulate the changing of illumination; the experiment condition was represented by original-day.
Figure 7 shows the homing vector fields for the warping method and the proposed method. (1, 4), (7, 13) and (5, 9) in the capture grid were selected as goal positions, and the corresponding experiment conditions were original-original, original-arboreal and original-day, respectively. In
Figure 7, the current positions are marked by blue squares, and the goal positions are marked by red squares. The homing direction is denoted by the line put out from the blue square.
Figure 8 shows the AE results for two homing methods. The experiment conditions and goal positions are the same as the settings of
Figure 7. The gray scale of each grid indicates the AE value of the corresponding (x, y) position in the capture grid of the database. Its changing from black to white represents the value ranging from 0 to the maximum of AE computed by the two methods. For observing, we change the threshold of white to 100 in the experiments. From
Figure 7 to
Figure 8, we can draw the following conclusions: Most of the homing directions computed by our method are more accurate than those computed by warping method. The AE of our homing method is lower than that of the warping method on the whole.
Figure 7.
Homing vector fields. (a,c,e) The homing vectors generated by the warping method; (b,d,f) the homing vectors generated by the proposed homing method.
Figure 7.
Homing vector fields. (a,c,e) The homing vectors generated by the warping method; (b,d,f) the homing vectors generated by the proposed homing method.
Figure 8.
Angular error (AE) results. (a,c,e) The homing angular errors generated by warping method; (b,d,f) the homing angular errors generated by the proposed homing method.
Figure 8.
Angular error (AE) results. (a,c,e) The homing angular errors generated by warping method; (b,d,f) the homing angular errors generated by the proposed homing method.
Figure 9 shows the distribution of AHC according to the distance between C and H. The corresponding experiment conditions for
Figure 9a–c were original-original, original-arboreal and original-day, respectively. From
Figure 9, it can be seen from the changing trends of “P” and “PN” that the mismatching elimination step can effectively improves the homing performance. It also can be seen intuitively from the changing trends of “P” and “W” that the AHC of our homing method is superior to that of the warping method on the whole. In the three groups of experiments, the AHC of two methods is always above 0, which indicates that both methods have the ability to guide the robot to approach the goal position gradually. From
Figure 9a,b, although the change of a tall plant in the experiment scene leads to a slight decrease in AHC for two methods, our homing method still performs better. As shown in
Figure 9a,c, when the illumination of the experiment scene changes, the performance of the warping method drops dramatically, while the performance of our homing method drops slightly. In conclusion, the results show that our homing method has better robustness to the changes of the environment. In
Figure 9, we can see an interesting phenomenon: when the distance between C and H is approximately within the range 30 to 330 cm, the AHC of our method is closer to 1 than that of the warping method, which shows that the average AE of our homing method is smaller; when the distance between C and H is approximately within the range 360 to 390 cm, the AHC of our homing method is smaller than that of the warping method, which indicates that the average AE of our homing method is higher. The main reasons for this situation are as follows: (1) when the distance between C and H is short (30 to 330 cm), there are more correct matching landmarks due to minor differences between the two images; consequently, the proposed mismatching elimination algorithm can effectively remove the mismatching landmarks, and our homing algorithm can get higher calculation accuracy; (2) when the distance between C and H is far (360 to 390 cm), the number of matching landmarks is smaller, and among them, there are more mismatching landmarks. For this reason, the proposed algorithm cannot effectively eliminate the mismatching landmarks, which makes the calculation accuracy of our homing algorithm decrease significantly.
Figure 10 shows the RR for the two methods under the three experiment conditions. “P” represents the proposed homing method; “PN” represents the proposed homing method without mismatching elimination step; and “W” represents the warping method. Trying to avoid the influence of randomness, we chose (1, 4), (1, 12), (5, 9), (8, 3) and (7, 13) in the capture grid of the image databases as goal positions, which are uniformly distributed in the experiment scene. From
Figure 10, it can be seen from the bar chart of “P” and “PN” that the mismatching elimination step can effectively improve the RR of our homing method. There are 15 different goal positions tested; compared to the warping method, our method performs better at 13 goal positions. From
Figure 10a,b, although the RR for the two methods drops slightly with the changing of a tall plant in the experiment scene, our homing method still performs better. The performance for the two methods is greatly influenced when the illumination changes in the experiment scene, as shown in
Figure 10a,c. Especially for the warping method, the homing performance declines dramatically. The results of RR turn out to be the same as those of AHC: compared to the warping method, our homing method has better robustness to the changes of the environment in the scene.
Figure 9.
Average homeward component (AHC) results. (a–c) The distribution of AHC under the experiment conditions: original-original, original-arboreal and original-day. P, proposed homing method; PN, proposed homing method without a mismatching elimination step; W, warping method.
Figure 9.
Average homeward component (AHC) results. (a–c) The distribution of AHC under the experiment conditions: original-original, original-arboreal and original-day. P, proposed homing method; PN, proposed homing method without a mismatching elimination step; W, warping method.
Figure 10.
Return ratio (RR) results. (a–c) The RR for five goal positions under the experiment conditions: original-original, original-arboreal and original-day.
Figure 10.
Return ratio (RR) results. (a–c) The RR for five goal positions under the experiment conditions: original-original, original-arboreal and original-day.
4.5. Homing Trials in a Real Scene
In order to further evaluate the performance of our method in practice, experiments were conducted in a real scene. We selected the intelligent robot lab of Harbin Engineering University as the experiment scene. The surroundings of the trial area are shown in
Figure 11. The tracked mobile robot introduced in
Section 4.1 was used in the trials. We randomly chose four goal positions, which were uniformly distributed in the trial area. Five current positions for each goal position spaced evenly throughout the area were selected for tests. The robot took the panoramic image at its current position, compared it to the goal image stored in memory and computed the homing angles separately by the proposed method and the warping method. After that, in the homing direction, the robot moved a step at the fixed length of 25 cm. In the trials, the above process would repeat until the robot reached a place within the range of 30 cm of the goal position or its movement distance was more than half of the circumference of the trial area, which was when the robot moves no more than 43 steps. If the robot can arrive at the goal position within the prescribed steps, the homing is successful; otherwise, the homing has failed. Because most stopping criteria based on image information are likely to lead the robot to oscillate around the goal position, the robot was manually stopped once it reached the goal area.
Figure 11.
Robot trial environment in the real scene.
Figure 11.
Robot trial environment in the real scene.
Figure 12,
Figure 13,
Figure 14 and
Figure 15 show the trajectories of the robot for the two methods, with tables listing the statistics of the number of homing steps
N and the average angular errors
σ(°) in each trial. The goal area is indicated by the red circle. “CP” represents the current position. Red lines represent the trajectories of the proposed method. Blue lines represent those of the warping method. As shown in
Figure 12,
Figure 13,
Figure 14 and
Figure 15, most homing trajectories for the warping method are more curved than those for our method. In total, 20 homing trials were carried out, 17 of which suggest that the average angular errors for our method are smaller; the number of total homing steps for the warping method is 312, while for our method, that number is only 292. Both the trajectories and statistics indicate that the homing angles computed by our method are more accurate, and the movement distance is shorter.
Figure 12.
Robot homing Trial 1. Top left: the panorama of the goal position; top right: the homing trajectories for five different current positions; the table below: the number of homing steps and the average angular error for each current position. CP, current position.
Figure 12.
Robot homing Trial 1. Top left: the panorama of the goal position; top right: the homing trajectories for five different current positions; the table below: the number of homing steps and the average angular error for each current position. CP, current position.
Method | CP1 | CP2 | CP3 | CP4 | CP5 |
---|
N | σ | N | σ | N | σ | N | σ | N | σ |
---|
Warping | 11 | 24.54 | 13 | 21.12 | 17 | 15.03 | 20 | 19.14 | 16 | 18.78 |
Proposed | 10 | 6.34 | 13 | 11.57 | 16 | 5.81 | 20 | 15.43 | 15 | 6.47 |
Figure 13.
Robot homing Trial 2.
Figure 13.
Robot homing Trial 2.
Method | CP1 | CP2 | CP3 | CP4 | CP5 |
---|
N | σ | N | σ | N | σ | N | σ | N | σ |
---|
Warping | 5 | 9.66 | 16 | 15.23 | 14 | 11.79 | 17 | 19.09 | 14 | 20.19 |
Proposed | 5 | 6.47 | 15 | 11.42 | 15 | 14.92 | 14 | 9.29 | 12 | 8.31 |
Figure 14.
Robot homing Trial 3.
Figure 14.
Robot homing Trial 3.
Method | CP1 | CP2 | CP3 | CP4 | CP5 |
---|
N | σ | N | σ | N | σ | N | σ | N | σ |
---|
Warping | 6 | 8.01 | 17 | 10.65 | 18 | 14.79 | 21 | 23.82 | 11 | 13.89 |
Proposed | 6 | 8.13 | 17 | 8.07 | 20 | 16.24 | 20 | 11.89 | 10 | 5.10 |
Figure 15.
Robot homing Trial 4.
Figure 15.
Robot homing Trial 4.
Method | CP1 | CP2 | CP3 | CP4 | CP5 |
---|
N | σ | N | σ | N | σ | N | σ | N | σ |
---|
Warping | 13 | 15.13 | 14 | 12.93 | 27 | 31.89 | 23 | 15.99 | 19 | 12.14 |
Proposed | 12 | 9.50 | 13 | 9.89 | 20 | 15.22 | 21 | 11.32 | 18 | 5.29 |