**4. Path planning: taking into account remote sensing applications**

### **4.1 Path planning in two dimensions with patrolling speed modification**

During the examination a route which ensures that each territorial unit, the socalled pixel, was chosen and only detected once during the cycle time of the patrol. Paths can be displayed in several forms as shown in **Figure 4**, but the equivalent is essential in the case of the fulfillment of the previous condition. The initial speed of the patrolling of the autonomous system is taken to be 60 km/h, and then it increased by 30 km/h up to 180 km/h. To examine the differences, the author takes the values of **Table 1**.

Defining the values of the basic case, "A" means that the area A = 576 km<sup>2</sup> divided into 9 km<sup>2</sup> ; taking AA = 64 units of floor area, we got the so-called pixels, which look like a chessboard. When an AA area unit has been flown at 60 km/h, the observation time is to = l/vpA = 3 km/60 km/h = 0.05 h, so that is 3 min. The length of the total route Lp = 64 × 3 km = 192 km long, which takes the next tp = LpA/ vp = 192 km/60 km/h = 3.2 h, that is, 192 min.

It can be seen from the values in the table that, by increasing the speed, the ratio of the observation time to the complete route is not changed (Ro = 1/64).

**109**

**Value event**

*configuration.*

**Figure 4.**

**Table 1.**

*non-observation time.*

**vp (km/h)**

**Hp (m)** **α (o**

**) Ao (km2 )**

*Path Planning Optimization with Flexible Remote Sensing Application*

The non-observation time frequency changes exponentially, the exponent is negative. In security checks, this result could be acceptable, but not in case of other examples like fire detection. The reason for this is that the fire increases constantly from the ignition time, so the burnt area changes exponentially. In the case of wildfires, it can be stated that the detection must be done within 15 min [25–27]. Continuing with the logic of the table, it can be calculated that it can only be

*Effects of changing speed of patrol for the observation time per a pixel and for the rate of observation and* 

detection cannot be increased (**Figure 5**).

or exceeds the all cost of the patrolling.

provided at extremely high speed (vp > 720 km/h). Based on the information above, it can be determined that by increasing the speed of the patrol, the efficiency of the

**l (km) Lp (km) tp**

A 60 0 180 9 3 192 192 3 189 1/64 B 90 0 180 9 3 192 128 2 126 1/64 C 120 0 180 9 3 192 96 1.5 94.5 1/64 D 150 0 180 9 3 192 78 1.3 76.7 1/64 E 180 0 180 9 3 192 64 1 63 1/64

*Examples of path planning with different pathway configurations for patrol. With constant patrol speed, the time of observation is equivalent in each pixel as well as equivalent to the length of total patrol route in each* 

**(min)**

**to (min)**

**tblind (min)**

**Ro (−)**

The purpose of patrolling is to provide faster detection than the signals of the citizens. This allows police officers to investigate hot trail or firefighters to begin the intervention earlier. The result of it is a faster response and more saved values. If the patrolling can result faster signal, it can be considered as an effective method. Professionally, this approach is obviously true; however, the higher efficiency in the point of national economy view is not proven by this method. It is effective at national economy level only in that case if the increase of the saved values reaches

To optimize the autonomous system's path planning, we should examine what happens if the camera's angle view is changed. For it we have to take the values from **Table 2**. We suppose the speed of patrolling, the maximum value of the patrolling speed based on **Table 1**, so the value is 180 km/h. We should also take other special

**4.2 Using remote sensing: increasing the camera's angle of view**

*DOI: http://dx.doi.org/10.5772/intechopen.86500*

*Path Planning Optimization with Flexible Remote Sensing Application DOI: http://dx.doi.org/10.5772/intechopen.86500*

#### **Figure 4.**

*Path Planning for Autonomous Vehicles - Ensuring Reliable Driverless Navigation...*

is the size of the pixel.

Based on the above, we have the following data:

• vp = patrol speed of the autonomous systems.

• Ao = size of the observed area in the given case.

• tblind = non-observation time per a pixel (blind time).

• Ro = rate of observation and non-observation time per a pixel.

During the assumption the camera on board has an angle of view that allows a simultaneous viewing of a 3 km × 3 km area at a given moment. In this test, we increase the speed of patrolling within reasonable limits, and next we increase the angle of view of the camera. Our aim is to determine how the observed and the blind area changes to an arbitrary point and what further conclusions can be drawn

**4. Path planning: taking into account remote sensing applications**

**4.1 Path planning in two dimensions with patrolling speed modification**

During the examination a route which ensures that each territorial unit, the socalled pixel, was chosen and only detected once during the cycle time of the patrol. Paths can be displayed in several forms as shown in **Figure 4**, but the equivalent is essential in the case of the fulfillment of the previous condition. The initial speed of the patrolling of the autonomous system is taken to be 60 km/h, and then it increased by 30 km/h up to 180 km/h. To examine the differences, the author takes

Defining the values of the basic case, "A" means that the area A = 576 km<sup>2</sup>

which look like a chessboard. When an AA area unit has been flown at 60 km/h, the observation time is to = l/vpA = 3 km/60 km/h = 0.05 h, so that is 3 min. The length of the total route Lp = 64 × 3 km = 192 km long, which takes the next tp = LpA/

of the observation time to the complete route is not changed (Ro = 1/64).

It can be seen from the values in the table that, by increasing the speed, the ratio

; taking AA = 64 units of floor area, we got the so-called pixels,

: total observation area.

• A = 576 km2

• AEA = 3 km × 3 km = 9 km2

• Hp = altitude of the patrol.

• l = side length of a pixel.

from the trend of change.

the values of **Table 1**.

vp = 192 km/60 km/h = 3.2 h, that is, 192 min.

divided into 9 km<sup>2</sup>

• tp = total cycle time of the patrol.

• to = observation time per a pixel.

• Lp = total length of the patrol.

• α = focus angel of the camera.

**108**

*Examples of path planning with different pathway configurations for patrol. With constant patrol speed, the time of observation is equivalent in each pixel as well as equivalent to the length of total patrol route in each configuration.*


#### **Table 1.**

*Effects of changing speed of patrol for the observation time per a pixel and for the rate of observation and non-observation time.*

The non-observation time frequency changes exponentially, the exponent is negative. In security checks, this result could be acceptable, but not in case of other examples like fire detection. The reason for this is that the fire increases constantly from the ignition time, so the burnt area changes exponentially. In the case of wildfires, it can be stated that the detection must be done within 15 min [25–27]. Continuing with the logic of the table, it can be calculated that it can only be provided at extremely high speed (vp > 720 km/h). Based on the information above, it can be determined that by increasing the speed of the patrol, the efficiency of the detection cannot be increased (**Figure 5**).

The purpose of patrolling is to provide faster detection than the signals of the citizens. This allows police officers to investigate hot trail or firefighters to begin the intervention earlier. The result of it is a faster response and more saved values. If the patrolling can result faster signal, it can be considered as an effective method. Professionally, this approach is obviously true; however, the higher efficiency in the point of national economy view is not proven by this method. It is effective at national economy level only in that case if the increase of the saved values reaches or exceeds the all cost of the patrolling.

#### **4.2 Using remote sensing: increasing the camera's angle of view**

To optimize the autonomous system's path planning, we should examine what happens if the camera's angle view is changed. For it we have to take the values from **Table 2**. We suppose the speed of patrolling, the maximum value of the patrolling speed based on **Table 1**, so the value is 180 km/h. We should also take other special

**Figure 5.**

*Correlation of patrol speed and time of patrol cycle (left) and a variation of patrol route planned for autonomous systems (right).*


#### **Table 2.**

*The effect of changing camera angle for the observed part of the area, demonstrating the theory with 1500 m path altitude.*

circumstances regarding the camera's view angle to understand the process better. Even if the patrol example in the previous subchapter was worked out at ground level, in **Table 2** the author counted with 1500 m altitude. It is performed to demonstrate with good visibility how the camera angle should change to be able to observe more than only one pixel at the same time.

The easiest way to change observation parameters is that to double the side length of the pixels, which means the territory becomes four times bigger than before. This process shows the development direction of the method. With this step we jump from the two-dimensional flat area to the three-dimensional space area that can be seen in the next subchapter even if in this moment this assumption serves only the more demonstrative understand.

It can be seen that by increasing the angle of view, the ratio of the time under observation increases exponentially comparing to the total flight time. Nonobservation time reduces in the same way as well as the non-observed area but with the opposite direction as shown in **Figure 6**.

The 15 min criteria as the tipping point of the effectiveness can be satisfied at the case of line "C" in **Table 2** with α = 1510 camera angle. In this case the value of the rate of observed area and non-observed area is ¼. By increasing the observation angle, the observed area unit increased as shown in **Figure 7**.

**111**

*Path Planning Optimization with Flexible Remote Sensing Application*

*Changing camera angle moves the flight path in to the centre of the observed area.*

Since the sample area is delimited, the centre of the larger area unit—4 pixels, than 16 pixels—as well as the trend of the path change moves also toward to the centre of the area. In the "D" case of **Table 2**, we can see that, under certain conditions, by increasing the angle of view, the area can be monitored continuously. In conclusion, by increasing the camera's angle of view, the efficiency of the detection

Even if we used 1500 m altitude to better understand the process, it is easy to accept that the method works at non-zero but minimal altitude too. We can assume a 2–3 m high installed camera on autonomous systems like an unmanned ground vehicles (UGV), but in this case the change of camera angel is very minimal. Since the assumed speed is 180 km/h, it is much easier to take an aerial autonomous system like unmanned aerial vehicle (UAV) for this example. This assumption signs

**4.3 Extending the possibility of patrolling by remote sensing to the third** 

As a next step, we can unlock the criteria for monitoring in two-dimensional area or standard but relatively at low-altitude (1500 m) observation. Based on it we can examine how the results change if we extend the possibility of patrolling to the third dimension. In this case we use the aerial autonomous systems like UAVs or drones as it was explained in the previous subchapter where 1500 m altitude was used. In this example we assume the same observation area that is 576 km<sup>2</sup>

same maximum patrol speed that is 180 km/h, and the standard camera angle view that is 90°. However, we modify now the altitude of the flight path using 1500 m basic level—as it was in the previous subchapter—and raise it with double steps as well as 1500, 3000, 6000, and 12,000 m. Based on these conditions, the results are

It can be seen that by increasing the flight altitude, the ratio of the time under observation increases exponentially comparing to the total flight time. Non-observation time reduces in the same way but with the opposite direction as shown in **Table 3**.

, the

*DOI: http://dx.doi.org/10.5772/intechopen.86500*

*The effect of changing camera angle for the flight path.*

can increase significantly.

**Figure 6.**

**Figure 7.**

**dimension**

shown in **Table 3**.

also the direction of the next examination.

*Path Planning Optimization with Flexible Remote Sensing Application DOI: http://dx.doi.org/10.5772/intechopen.86500*

**Figure 6.** *The effect of changing camera angle for the flight path.*

**Figure 7.**

*Path Planning for Autonomous Vehicles - Ensuring Reliable Driverless Navigation...*

circumstances regarding the camera's view angle to understand the process better. Even if the patrol example in the previous subchapter was worked out at ground level, in **Table 2** the author counted with 1500 m altitude. It is performed to demonstrate with good visibility how the camera angle should change to be able to observe

*The effect of changing camera angle for the observed part of the area, demonstrating the theory with 1500 m* 

**l (km) Lp**

A 180 1500 90 9 3 192 64 1 63 1/64 B 180 1500 126 36 6 96 32 2 30 4/64 C 180 1500 151 144 12 48 16 4 12 16/64 D — 1500 165 576 24 — — Cont. — 64/64

**(km)**

**tp (min)**

**to (min)**

**tblind (min)** **Ro (−)**

The easiest way to change observation parameters is that to double the side length of the pixels, which means the territory becomes four times bigger than before. This process shows the development direction of the method. With this step we jump from the two-dimensional flat area to the three-dimensional space area that can be seen in the next subchapter even if in this moment this assumption

It can be seen that by increasing the angle of view, the ratio of the time under

observation time reduces in the same way as well as the non-observed area but with

The 15 min criteria as the tipping point of the effectiveness can be satisfied at the

of observed area and non-observed area is ¼. By increasing the observation angle, the

camera angle. In this case the value of the rate

observation increases exponentially comparing to the total flight time. Non-

more than only one pixel at the same time.

serves only the more demonstrative understand.

the opposite direction as shown in **Figure 6**.

observed area unit increased as shown in **Figure 7**.

case of line "C" in **Table 2** with α = 1510

**110**

**Value event**

**Figure 5.**

**Table 2.**

*path altitude.*

**vp (km/h)**

*autonomous systems (right).*

**Hp (m)** **α<sup>D</sup> ( 0 )**

**Ao (km2 )**

*Correlation of patrol speed and time of patrol cycle (left) and a variation of patrol route planned for* 

*Changing camera angle moves the flight path in to the centre of the observed area.*

Since the sample area is delimited, the centre of the larger area unit—4 pixels, than 16 pixels—as well as the trend of the path change moves also toward to the centre of the area. In the "D" case of **Table 2**, we can see that, under certain conditions, by increasing the angle of view, the area can be monitored continuously. In conclusion, by increasing the camera's angle of view, the efficiency of the detection can increase significantly.

Even if we used 1500 m altitude to better understand the process, it is easy to accept that the method works at non-zero but minimal altitude too. We can assume a 2–3 m high installed camera on autonomous systems like an unmanned ground vehicles (UGV), but in this case the change of camera angel is very minimal. Since the assumed speed is 180 km/h, it is much easier to take an aerial autonomous system like unmanned aerial vehicle (UAV) for this example. This assumption signs also the direction of the next examination.
