Estudio comparativo de datos empíricos obtenidos de sensores utilizados para medir la distancia de obstáculos

2.1. Sensors and characteristics

Two sensor types (ultrasonic and infrared) were used in this work with the aim of identifying their performance in distance detection.

The ultrasonic sensor (HC-SR04), by Corporate Computer, has an operating range of 2 to 400 cm. It has two inputs and two outputs for VCC, TRIG, ECHO, and GND signals. The angle to the normal line of the obstacle surface cannot exceed 15°. Therefore, in this work, the obstacle had to be orthogonal to the surface of the sensor, i.e., at a right angle (90°) to the sensing surface of the sensor. The ultrasonic sensor was fed with 3 V and was connected to ESP8266 device. The trigger input (TRIG) was used to send a series of pulses over eight cycles clocked at 40 kHz.

Fig. 1 shows the basic operation of the sensor. The ECHO output measures the time interval between sending the TRIG signal and receiving the ECHO signal, so the pulse width delivered by the output is used to determine the distance ¹⁶.

Figure 1: Timing diagram of signals in the ultrasonic sensor (17)

The ultrasonic sensor sends a TTL pulse with a duration of 10 us via the TRIG pin. A set of pulses clocked at 40 kHz are sent at the end of the TTL pulse (acoustic burst). Finally, the ECHO pin recovers the transmitted signal, and it sends a pulse with a specific width, which can take values from 150 to 25 ms. The distance d can be calculated using Eq. (1).

where, t is the time interval between sending the TRIG signal and receiving the ECHO signal (i.e., the space between the acoustic bursts and the reflected signal). Two scenarios were analyzed for the ultrasonic sensor: the first with the obstacle frontally aligned to the sensor (frontal) and the second with the obstacle non-frontally aligned (lateral), in order to obtain a map with the view field of sensor.

The GP2Y0A21YK0F infrared sensor by Sharp has an analog output and is controlled and fed by the ESP8266 device. The Vo output measures the time interval between sending the trigger signal and receiving it. Thus, the distance is calculated by the pulse width delivered by the output ¹⁸. The sensor performs various measurements, as shown in Fig. 2.

Figure 2: Timing diagram of signals in the infrared sensor (18)

To obtain the distance between sensor and obstacle, the equation to convert the ADC value into the estimated distance was determined. The theoretical curve provided by the manufacturer is shown in Fig. 3. It relates the distance to the object with the output voltage.

Furthermore, the behavior of the infrared sensor was determined. To this effect, a flat obstacle was positioned orthogonally to the sensor and then moved centimeter by centimeter. Fig. 4 shows the results of the measured distances vs. the ADC values for the experiment. These results provided the data curve and its representative Eq. (2).

This equation was used for the first study of the sensor. The numerical value given by the sensor was recorded during this research and compared against a theoretical distance. x represents the value generated by the ADC converter, which is denoted as gp2y0a21Val in the program environment.

2.2. Experiments

The sensor's behavior was studied in two scenarios: frontal and lateral. Experiments were conducted in a controlled environment within an Internet of Things (IoT) laboratory, which has an approximate area of 6 x 6 m. No additional objects were present which could interfere with the measurements. The obstacle used was a 22 x 27 cm rectangle. In addition, for the infrared sensor, a flat white surface was used to optimize wave reflection.

To ensure the repeatability and precise control of distances and angles, a programmable system based on the ESP8266 was used. This system followed predefined trajectories, allowing for systematic measurements. Markers were placed on the ground at regular intervals to verify the actual distances between the sensor and the obstacle. Table I details the number of measurements taken for each point, with a total of 47 positions in 2 cm steps (0 to 92 cm) for the infrared sensor and 93 positions in 5 cm steps (0 to 460 cm) for the ultrasonic sensor. In this work, a test refers to an experiment involving measurements (10 per position point), and a position point is one of the possible locations of the obstacle relative to the sensor.

Figure 3: Timing diagram of signals in the ultrasonic sensor 18

Figure 4: Computed and measured distances for different values of the ADC of sensor

2.2.2. Lateral situation

To determine the detection response of sensors to non-frontal situations, the obstacle must be placed in the extension of the sensors and diagonally displaced to the right.

In this experiment, each obstacle is moved along the corresponding range, i.e., from 0 to 460 cm (5 cm steps) for the ultrasonic sensor and from 0 cm to 92 cm (2 cm steps) for the infrared sensor. The program sends a notification when the obstacle is out of the measurement range and becomes invisible for sensor. Fig. 5 shows the positioning of the sensor and the obstacle. A real measurement of the distances is performed for each point and fed to the program. This process is repeated for the subsequent distances. The program computes the sensor's angle with respect to the obstacle. Here, a right angle indicates whether the sensor is able to detect objects located along the diagonal, which is analogous to the left diagonal by the symmetry of sensors.

Figure 5: Lateral positioning of the obstacle

The values are stored in a dynamic array, and they are presented as a text file in the following format: d_time; distanceA; distanceB; distanceC; angle. The angle is obtained using Eq. (3).

3.1. Ultrasonic sensor

The HC-SR04 sensor can detect an obstacle if it is orthogonal to its field of view, with a theoretical angular tolerance of 15°. However, the sensor cannot identify an obstacle that is not orthogonal. The sensor is directional and provides accurate distance estimations in frontal scenarios, as shown in Fig. 6a. The distance measured in frontal situations (0° angle) shows excellent correspondence with the real distance, forming a linear relationship. Moreover, in most measurements (Fig. 6b), the error remains below 1 %, except for the estimation of shorter distances (0 to 90 cm), where it exceeds 1 % but stays below 5 %.

Figure 6: Ultrasonic sensor in frontal situations

Studying the vision range allows understanding the sensor's ability to detect diagonal obstacles (Fig. 7). The results show better distance detection when the obstacle is located frontal to the sensor at large distances close to the 400 cm limit. This has to do with the directivity of the ultrasonic sensor in radiating the power of signal, provided that it is not disturbed by its environment. Distance estimation can be performed at shorter distances, but only when the obstacle is diagonally positioned relative to the sensor. For example, it is possible to detect objects at 200 cm and 10°, or at 50-150 cm and 20°.

Figure 7: Ultrasonic sensor in lateral situations

The values show a defined tendency, without significant variations. Measurement accuracy is also a strength of this sensor; the error is low - almost negligible - along its range of use. The operating range specified by the manufacturer is therefore validated. However, the sensor is capable of operating beyond the theoretical limit.

Some advantages of the ultrasonic sensor include an operating range of 2 to 400 cm, good accuracy, high directivity, and ease of use. On the other hand, one of its drawbacks is its inability to detect obstacles that are significantly offset from its field of view, a phenomenon that becomes more pronounced as the distance increases.

3.2. Infrared sensor

The GP2Y0A021YK infrared sensor does not allow for obstacle detection at long distances when compared to its ultrasonic counterpart, since its detection range is limited to 80 cm according to the manufacturer's data. However, the sensor cannot be used throughout the recommended operating range. The experiment conducted in this study showed that the sensor can only detect distances between 10 and 60 cm. The use of Eq. (2) implies some error, which is more considerable for distances between

Figure 8: Infrared sensor in frontal situations

Fig. 8 presents some tests carried out on the infrared sensor, altering the distance to the obstacle in frontal positions. Within the operating range (10 to 80 cm), estimation via Eq. (2) is adequate for applications requiring lower accuracy. However, in some tests (e.g., 10, 37, 45, or 80 cm), the error is high (close to 15%). As shown in the figure, distance measurement errors become excessively high outside the operating range.

On the other hand, Fig. 9 presents the sensor's performance in lateral scenarios. This sensor provides accurate distance estimations at angles of up to approximately 20° along most of its operating range. Even at short distances, the angle can reach nearly 30°. Different measures were taken, and a good correlation between them was observed. The red line in Fig. 9 shows the average for all measurements, representing the estimation tendency of the sensor.

The main advantage of the infrared sensor is its good detection of obstacles in lateral situations. However, it has some drawbacks, such as difficulties in obtaining a realistic equation for distance estimation, medium accuracy along the theoretical operational range, and low estimation distances (80 cm maximum limit).

Figure 9: Infrared sensor in lateral situations

3.3. Statistical study

Using Python, several statistical studies were performed. A linear correlation was established between the two sensors in order to quantify their linear relationship. Fig. 10 presents a scatter diagram with linear adjustment, with the ultrasonic sensor on the horizontal axis and the infrared sensor on the vertical one.

Figure 10: Scatter diagram with linear adjustment

The two mean distances increase simultaneously at a constant rate. The scatter plot in Fig. 10 shows a positive linear relation between the distance variables measured by the sensors. However, this is only the case for distances between 10 and 50 cm measured by the infrared sensor. Outside this range, the relation is not exactly linear anymore. In this vein, the different correlation coefficients were determined, and a distribution plot was elaborated for both sensors (Fig. 11). This plot shows that the data distribution has a non-normal tendency and is slightly more uniform.

Figure 11: Distribution of values for both sensors

Fig. 12 presents the results of a study conducted to evaluate the distribution of the residuals, which are aligned along a straight line. However, very slight biases can be observed in the tails. The data lie close to the red line, indicating a linear correlation.

Figure 12: Quantile diagram for the ultrasonic sensor

An analysis was performed to qualify the results and compute the correlation coefficients with several methods: Pearson, Spearman, and Kendall. In all cases, a more sensitive result was observed with regard to the extreme values, as well as a good correlation for most values.

For the ultrasonic sensor, the linear association is very high for all three methods, which confirms that the measured results are close to the theoretical values. The correlation coefficients computed for the ultrasonic sensor are as follows:

• Pearson correlation: 0.999

• Spearman correlation: 0.999

• Kendall correlation: 0.998

On the other hand, the infrared sensor exhibits a lower linear association than its ultrasonic counterpart, but it remains over 90 %, which is also a high value. The correlations for the infrared sensor are presented below:

• Pearson correlation: 0.952

• Spearman correlation: 0.982

• Kendall correlation: 0.926

Good results were obtained since the correlation for the infrared sensor was evaluated along its operating range, which shares many similarities with that of the ultrasonic sensor. It is possible to obtain lower correlations by comparing the infrared sensor used against other alternatives with different operating ranges.