2.1 Model layers

The calculation of the model combined cost surface of passability consists of several layers of the task variables that are defined in the following text:

1. Ground surface layer

The ground surface layer forms a basis for further analysis of the model. Its cost surface of passability (Pnp1) consists of sublayers representing the types of ground surface as follows, described in [11–13]:

a. Plant and soil cover

Figure 1. The creation of the combined cost surface of passability (source: own).


1. Ground surface layer (Pnp1, HF1)

2. Elevation layer (VF2)

3. Weather layer (HF3)

shown in Figure 1.

2.1 Model layers

1. Ground surface layer

a. Plant and soil cover

Figure 1.

82

surface as follows, described in [11–13]:

The creation of the combined cost surface of passability (source: own).

4. Enemy situation layer (HF4)

5. Friendly forces and equipment layer of (HF5)

The metrics of criterion evaluation are different for each layer in relation to its character and composition. The basic data for its calculation are cell dimensions, the average movement speed of a selected element on a given type of the ground surface that moves across the cell, and the resistance of the factor under consideration. The value calculated through the combination of Pnp1 and all layers of the model indicates the combined time of covering a given cell, influenced by all terrain and situation factors, in the form of the combined cost surface of passability (SPnp),

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The calculation of the model combined cost surface of passability consists of

The ground surface layer forms a basis for further analysis of the model. Its cost surface of passability (Pnp1) consists of sublayers representing the types of ground

several layers of the task variables that are defined in the following text:

Based on its Pnp1, the effects of other layers of the model are derived.

2. Elevation layer

The hypsometry layer is formed by topography, which enters the calculation of SPnp through the vertical factor (VF2) of the terrain slope. Its definition can be formulated as a measure of demanding movement in the elevated terrain. SPnp1,2 is created by a multiple of Pnp1 with a value of VF2. It varies according to the type of movement as a vertical factor of the terrain slope for vehicles (VF2V) and for dismounted units (VF2C). The calculation of these factors is expressed by mathematical formulas (1) and (2). In the case of the movement of tracked or wheeled vehicles, it is possible to refer to the so-called linear influence of the terrain slope on the average speed of a given type of a vehicle. The vehicle engine load increases evenly with the rise in the terrain slope, and, under unchanged operating conditions, it causes a steady drop in speed. On the contrary, when driving downhill, the vehicle speed increases steadily. However, its gravity increase, given by the downhill driving and the pull of gravity, is usually broken by the driver using the braking system of the vehicle. The vertical factor of the terrain slope for vehicles (VF2V) is expressed by the mathematical formula as follows:

$$\forall F\_{2\mathcal{V}} = K\_{\mathcal{V}2\mathcal{V}} \times \mathcal{O} + 1 \tag{1}$$

The limiting passable terrain slope is set for tracked vehicles in the range of �30° to +30° and for wheeled vehicles of �30° to +20°, derived from [14–16]. Out of the range of these values, the terrain slope in the model is assessed as impassable, with VF2 = 0. The course of VF2V has a linear character given by constant value KV2V = �0.004.

The difficulty of the movement of a dismounted element in the field has a nonlinear course as opposed to vehicles. The terrain slope (ω) affects the dismounted movement downhill or uphill differently depending on the topography and the safe movement controllability. Its difficulty in walking uphill increases exponentially as the slope increases. When walking downhill, it drops down up to 20°, when it is equal to the difficulty of movement on the flat ground. When walking downhill with the angle of slope of more than 20°, the difficulty increases again with the increasing slope. Such a course is caused by a degree of gravity that facilitates the movement at first. However, when the terrain slope is more than 20°, it forces the dismounted movement of individuals to brake in order to maintain a safe control over their movement. The influence of the terrain slope on the dismounted movement is expressed by the vertical factor of the terrain slope for dismounted movement (VF2C). The coefficient of the vertical factor for dismounted individuals (KV2C) is included in its calculation shown in Figure 2, which represents the degree of difficulty of the dismounted movement for a given terrain slope. Its values have been borrowed from the thesis developed by Lenka Mezníková, described in [17]. The limiting passable terrain slope for the dismounted movement is set in the range of �50° to +50°.

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• For the dismounted element: O3.1C = VF2C

even impassable for the dismounted element.

4. The enemy situation layer

The value of HF3.2 with different rainfall amounts.

equipment.

Table 1.

85

formula is used as follows:

Model of the Optimal Maneuver Route DOI: http://dx.doi.org/10.5772/intechopen.85566

mula is used as follows:

For the movement of tracked and wheeled vehicles, the derived mathematical

For the movement of the dismounted element, the derived mathematical for-

The limiting passable snow thickness for the dismounted element is set for 90 cm of snow since a thicker layer of snow is negotiable with great difficulties or

The model of the movement route for forces and equipment evaluates the effects of rainfall only for tracked and wheeled vehicles that move off the paved roads. The limitation of the terrain passability due to rainfall is generally assessed in four steps based on the precipitation amount for the purpose of creating a movement route in the model. The degree of limitation of individual steps is derived from the reduction in vehicle climbing performance, which defines the approximated reduction in vehicle climbing performance up to 50% when moving on a muddy soil surface. The muddy soil surface is defined generally as a precipitation amount larger than 40 mm in 3 days. Based on the meteorological forecast or the measurement of the abovementioned precipitation amounts, the model user can set a horizontal

The enemy situation layer evaluates the safe passability of the area, depending on the possibilities of effective fire of his main weapons. It is created by the results of collecting the information on the enemy forces and equipment, which are defined in the model by their geographical position and the attributes of the tactical and technical characteristics of his weapons. From the location of their deployment, the area that is visible within the effective range of enemy weapon systems is then evaluated. Further, the model evaluates the danger area (which is impassable) of detected unexploded ammunition, improvised explosive devices (IEDs) or minefields, which is set based on the weight of detonating charge and the type of ammunition. The degree of danger expresses the degree of difficulty of covering the given area in the form of horizontal factor of the enemy situation (HF4). The database of forces and equipment enables the rapid editing of enemy forces and

HF3.2 Rainfall amounts 0 impassable Larger than 80 mm 0.25 Larger than 60 mm 0.5 Larger than 40 mm 0.75 Larger than 20 mm 1 without an effect Smaller than 20 mm

� <sup>O</sup>3:1P=<sup>K</sup> � <sup>ω</sup> (3)

HF3:1<sup>C</sup> ¼ 1 � ð Þ� K3:1<sup>C</sup> � L3:<sup>1</sup> ð Þ 1 � O3:1<sup>C</sup> (4)

HF3:1P=<sup>K</sup> ¼ 1 � K3:1P=<sup>K</sup> � L3:<sup>1</sup>

rainfall factor (HF3.2), which attains the values listed in Table 1.

#### Figure 2.

Coefficient of vertical factor for dismounted movement (source: own).

The KV2C curve, shown in the graph in Figure 2, has been put through the third degree polynomial curve to generate a regression equation as follows:

$$K\_{V2C} = -0.0121 \left(\frac{\alpha}{10}\right)^3 + 0.0968 \left(\frac{\alpha}{10}\right)^2 + 0.3156 \frac{\alpha}{10} + 0.9933\tag{2}$$

The value of the regression equation reliability is 0.9875.

3. Weather layer

In the weather layer, snowfall and rainfall are taken into account as direct effects on the terrain passability. Both of these effects are characterized by the overall impact of its occurrence in [18], which can be defined in the model based on the weather forecast or meteorological radar outputs. Snowfall limits the terrain passability on the entire terrain area. On the roads, it reduces the adhesion of their surface to the chassis of moving vehicles, even on a thin layer of snow.

To calculate the possibilities of passability in the field with a zero slope, the coefficients of the snow layer influence (K3.1) related to particular types of moving elements were mathematically derived, as follows:


The combination of the influences of the terrain slope and the snow layer thickness implements the coefficient of the snow-covered topography (O3.1) in the calculation of HF3.1, which is differentiated according to the type of a moving element. O3.1 attains the following values:


• For the dismounted element: O3.1C = VF2C

For the movement of tracked and wheeled vehicles, the derived mathematical formula is used as follows:

$$HF\_{\text{3.1P/K}} = \mathbf{1} - \left(K\_{\text{3.1P/K}} \times L\_{\text{3.1}}\right) - \left(O\_{\text{3.1P/K}} \times \boldsymbol{\alpha}\right) \tag{3}$$

For the movement of the dismounted element, the derived mathematical formula is used as follows:

$$HF\_{\rm 3.1C} = \mathbf{1} - (K\_{\rm 3.1C} \times L\_{\rm 3.1}) - (\mathbf{1} - O\_{\rm 3.1C}) \tag{4}$$

The limiting passable snow thickness for the dismounted element is set for 90 cm of snow since a thicker layer of snow is negotiable with great difficulties or even impassable for the dismounted element.

The model of the movement route for forces and equipment evaluates the effects of rainfall only for tracked and wheeled vehicles that move off the paved roads. The limitation of the terrain passability due to rainfall is generally assessed in four steps based on the precipitation amount for the purpose of creating a movement route in the model. The degree of limitation of individual steps is derived from the reduction in vehicle climbing performance, which defines the approximated reduction in vehicle climbing performance up to 50% when moving on a muddy soil surface. The muddy soil surface is defined generally as a precipitation amount larger than 40 mm in 3 days. Based on the meteorological forecast or the measurement of the abovementioned precipitation amounts, the model user can set a horizontal rainfall factor (HF3.2), which attains the values listed in Table 1.

### 4. The enemy situation layer

The enemy situation layer evaluates the safe passability of the area, depending on the possibilities of effective fire of his main weapons. It is created by the results of collecting the information on the enemy forces and equipment, which are defined in the model by their geographical position and the attributes of the tactical and technical characteristics of his weapons. From the location of their deployment, the area that is visible within the effective range of enemy weapon systems is then evaluated. Further, the model evaluates the danger area (which is impassable) of detected unexploded ammunition, improvised explosive devices (IEDs) or minefields, which is set based on the weight of detonating charge and the type of ammunition. The degree of danger expresses the degree of difficulty of covering the given area in the form of horizontal factor of the enemy situation (HF4). The database of forces and equipment enables the rapid editing of enemy forces and equipment.


#### Table 1.

The KV2C curve, shown in the graph in Figure 2, has been put through the third

In the weather layer, snowfall and rainfall are taken into account as direct effects

on the terrain passability. Both of these effects are characterized by the overall impact of its occurrence in [18], which can be defined in the model based on the weather forecast or meteorological radar outputs. Snowfall limits the terrain passability on the entire terrain area. On the roads, it reduces the adhesion of their

To calculate the possibilities of passability in the field with a zero slope, the coefficients of the snow layer influence (K3.1) related to particular types of moving

The combination of the influences of the terrain slope and the snow layer thickness implements the coefficient of the snow-covered topography (O3.1) in the calculation of HF3.1, which is differentiated according to the type of a moving

surface to the chassis of moving vehicles, even on a thin layer of snow.

10 <sup>2</sup> <sup>þ</sup> <sup>0</sup>:<sup>3156</sup> <sup>ω</sup>

<sup>10</sup> <sup>þ</sup> <sup>0</sup>:9933 (2)

<sup>þ</sup> <sup>0</sup>:<sup>0968</sup> <sup>ω</sup>

degree polynomial curve to generate a regression equation as follows:

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10 <sup>3</sup>

The value of the regression equation reliability is 0.9875.

KV2<sup>C</sup> ¼ �0:<sup>0121</sup> <sup>ω</sup>

Coefficient of vertical factor for dismounted movement (source: own).

elements were mathematically derived, as follows:

• For the dismounted movement: K3.1C = 0.008

• For tracked vehicles: K3.1P = 0.01205

• For wheeled vehicles: K3.1K = 0.0192

element. O3.1 attains the following values:

• For tracked vehicles: O3.1P = 0.034

• For wheeled vehicles: O3.1K = 0.0576

84

3. Weather layer

Figure 2.

The value of HF3.2 with different rainfall amounts.

#### 5. Friendly forces and equipment layer

The model of the optimal movement route evaluates the influence of availability of fire support executed by friendly forces and equipment based on their current position and effective range of the main weapon system. The model evaluates these facts as a supporting factor for the ability to pass through the area affected by the enemy activity via HF5. HF5 expresses the degree of reduction in the impact of the enemy activity in terms of supporting the passage of the danger area of the task performance. The layer of friendly forces and equipment does not affect the passability of the area as a whole. It expresses only the ability or capabilities of friendly forces and equipment to support the maneuvering element by eliminating security risks. Thus, the combined cost surface of passability includes layers 1.4 and 5 only. The calculation of SPnp1.4,5 is then expressed by formula (5):

$$\text{LSI}\_{\text{sp1.4.5}} - \frac{P\_{\text{sp1.4}}}{\min(\text{l}\_s, HF\_4 \times IIF\_3)} \tag{5}$$

3.1 Influence of detected enemy combat activity in the past

surroundings are critical for this kind of evaluation.

attacks and incidents over the last 3 months

following average values:

Model of the Optimal Maneuver Route DOI: http://dx.doi.org/10.5772/intechopen.85566

weapon systems

surfaces)

87

observable by the enemy

3.3 Databases of system information

bases so that they can always be used quickly.

The information databases can be divided into:

carried weapon systems, and their effective range)

The past activity of the enemy includes the activity of his forces and equipment over the last 6 months, which can be divided according to the observed type of activity (laid minefields, barriers, IED, IDF, SAF, SVEST attacks, demonstrations, and other incidents). The geographical position, the type of activity or attack and its development, the frequency of repetition in the same areas, and the description of

The degree of threat to the safe movement through the area can be expressed by

enemy activity, active minefields and barriers, and the repeated occurrence of

the horizontal factor of enemy activity in the past HF4.2, which can acquire the

• HF4.2 = 0, an impassable area, at a distance of 500 m from the site of the

• HF4.2 = 0.5, at a distance of 1000 m from the site of the enemy activity and the repeated occurrence of attacks and incidents over the last 3 months

• HF4.2 = 1, without affecting the passability, at a distance of more than 1000 m from the site of the enemy activity, attacks, and incidents older than 3 months

This evaluation has already been described in a simplified fashion in the enemy situation layer. The model evaluates danger areas of the potential enemy conduct of effective fire depending on the visibility and effective range of the main weapons. The degree of threat to the safe movement through the area may be expressed by horizontal factor of the enemy firepower HF4.1, which attains the following values:

• HF4.1 = 0, impassable, enemy-observable area of an effective range of his

• HF4.1 = 0.5, an area at a distance of 1 to 1.5 multiple of the effective range of the enemy weapon systems in a strip of the area observable by the enemy

• HF4.1 = 1, a passable area with minimal predictable threat, at a distance of 1.5 multiple of the effective range of the enemy weapon system in the area

The system input information must be structured and stored in thematic data-

• The TTD of friendly military equipment and weapon systems (including width, length, clearance height, weight, maximum range, terrain passability,

• The characteristics of performance parameters of the dismounted element (including the speed of movement at different slopes and on different terrain

3.2 Influence of the current deployment of enemy forces and equipment

In the areas where any combat activity of the enemy is not and even was not detected in the past, its influence on the passability in the model is not evaluated.

#### 2.2 Combined cost surface of passability

The model of combined cost surface of passability (SPnp) is created by Pnp1 as a basis for its calculation and then by mathematical operations (division) of Pnp1 with HF and VF of individual layers. The SPnp calculation is then expressed by the mathematical formula as follows:

$$\text{SIP}\_{\text{sys}} \sim \frac{P\_{\text{post},s}}{\text{FF}\_{\text{>}} \times IIF\_{\text{>}} \times \min\left(0, IIF\_{\text{\downarrow}} \times IIF\_{\text{\downarrow}}\right)}\tag{6}$$

The result of the SPnp calculations is the difficulty of covering a given area in time affected by all the factors of the situation in the operation area shown in Figure 1.

## 3. Possibilities of the enemy activity influence

The enemy activity in the area of operation has the greatest influence on the planning of the movement route of forces and equipment along with the terrain passability. Estimating the future activity of the enemy is always a very complicated and intuitive matter for the analyst who processes it. Due to its uncertainty and variant implementation, it is impossible to create a mathematical algorithm that would accurately identify the intention of the enemy. However, it can be visualized based on the real terrain passability, including the weather attack, known deployment of enemy forces and equipment, and their activities in the past. The greatest deviations in the measurements were achieved outside paved roads, where hardly predictable impact of the microrelief, a driver's caution, and the dense vegetation of the terrain were evident.

5. Friendly forces and equipment layer

2.2 Combined cost surface of passability

3. Possibilities of the enemy activity influence

mathematical formula as follows:

expressed by formula (5):

not evaluated.

Figure 1.

the terrain were evident.

86

The model of the optimal movement route evaluates the influence of availability of fire support executed by friendly forces and equipment based on their current position and effective range of the main weapon system. The model evaluates these facts as a supporting factor for the ability to pass through the area affected by the enemy activity via HF5. HF5 expresses the degree of reduction in the impact of the enemy activity in terms of supporting the passage of the danger area of the task performance. The layer of friendly forces and equipment does not affect the passability of the area as a whole. It expresses only the ability or capabilities of friendly forces and equipment to support the maneuvering element by eliminating security risks. Thus, the combined cost surface of passability includes layers 1.4 and 5 only. The calculation of SPnp1.4,5 is then

Path Planning for Autonomous Vehicles - Ensuring Reliable Driverless Navigation…

In the areas where any combat activity of the enemy is not and even was not detected in the past, its influence on the passability in the model is

The model of combined cost surface of passability (SPnp) is created by Pnp1 as a basis for its calculation and then by mathematical operations (division) of Pnp1 with HF and VF of individual layers. The SPnp calculation is then expressed by the

The result of the SPnp calculations is the difficulty of covering a given area in time affected by all the factors of the situation in the operation area shown in

The enemy activity in the area of operation has the greatest influence on the planning of the movement route of forces and equipment along with the terrain passability. Estimating the future activity of the enemy is always a very complicated and intuitive matter for the analyst who processes it. Due to its uncertainty and variant implementation, it is impossible to create a mathematical algorithm that would accurately identify the intention of the enemy. However, it can be visualized based on the real terrain passability, including the weather attack, known deployment of enemy forces and equipment, and their activities in the past. The greatest deviations in the measurements were achieved outside paved roads, where hardly predictable impact of the microrelief, a driver's caution, and the dense vegetation of

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