**2. Basics of path planning**

#### **2.1 Path planning problems between two points**

The purpose of path planning is to find the best route according to the desired target function between two points. The target function may have different expectations, such as making the route as short as possible or as fast as possible (1). Assuming a two-dimensional plane area and ignoring any kind of disturbing circumstance, ideally shown in **Figure 1** (left) and assuming constant speed, it means in both cases the same path and the same time spent:

$$A \to B \langle s \Rightarrow \min; t \Rightarrow \min \rangle \tag{1}$$

**103**

*Path Planning Optimization with Flexible Remote Sensing Application*

*Path planning options between points of "A and "B" with two different possible routes.*

as shown in **Figure 2**. The quality of the different routes may be the same or different, but it is natural the better road quality allows faster progress, which means that

However, in case of different routes, choice is useless if there is no difference between them according to the target functions. The following options are available

1.The length and the quality of the two paths are the same (s1 = s2; q1 = q2).

2.The length of the two routes is different, but the quality is the same (s1 ≠ s2;

3.The length of the two routes is the same, but the quality is different (s1 = s2;

In general, the last one can be assumed. This gives new more opportunities, so the quality of the longer road can be better or worse than the shorter one and vice versa. In the latter case, when a longer road is combined with a poorer quality, it is clear this is not a choice. In the first case, when the quality of the longer road is

1.The quality of the road is better, but not so much as to compensate the choice

2.The quality of the road is better; however, its quality is able to compensate only

3.The quality of the road is so good that, despite the longer distance, we can

The above is a mere combination of two different routes. It is easy to notice that changing the conditions makes the above more complicated. Example, if we increase the optional routes or the possibility of road quality per each new route but even with changing the quality along one route, the solutions increase exponentially. It is easy to notice that the above assumptions provide an ever-increasing choice, which is in the direction of infinity. However, a large part of the choices can be excluded, so all of those are certainly in a less favorable direction than the one that has already been examined before. As an example, all new routes with the same or worse route quality compared to a route of a given length can be excluded if they

4.The length and quality of the routes are different (s1 ≠ s2; q1 ≠ q2).

better than the shorter one, you can get the following solutions:

for the loss of time resulting from the longer distance.

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

it takes less time to do the same route length.

q1 = q2).

**Figure 2.**

q1 ≠ q2).

with time gains.

achieve time gains.

are longer than the examined one.

for two routes based on their length and quality:

The simplest assumption in reality is very rarely found. In most cases the natural conditions make the simplest approach impossible, which means longer paths as shown in **Figure 1** (right) and longer access times. If the ideal path between the two points is not available, you have to choose from the other options available. The number of available options may vary between zero and infinity, but both lower and upper extremes should be excluded. At the theoretical starting point, the zero option means that there is no point in the task, and with the infinite possibility, we can only count on the theory. By excluding the two extremes, we find that the number of solutions varies from 1 to a large number. The only possible path, of course, does not give a choice. The first choice appears in case of two different paths

**Figure 1.**

*Path planning between points of "A" and "B" in ideal (left) and in natural (right) circumstances with only one option.*

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

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

victims in case of disaster.

called as an ideal case.

**2. Basics of path planning**

observed field can be wider and wider when passing the route. Following this logic, we can conclude that choosing a route is not merely premised on getting from one point to another one but rather on supervising and monitoring an area of responsibility. The purpose of the area monitoring is typical for safety reason, prevention and protection against criminals, swift forest fire detection, or offering first aid to

Following the path or monitoring, the area can be done by the traditional way meaning that the trained staff uses a vehicle; conversely it can be done in advanced way meaning that the presence of staff on board of the vehicle is no longer required. The latter can be interpreted as using the autonomous system. One of the advantages of autonomous systems is that we can eliminate human error by applying it. The effectiveness of the autonomous system should be examined under different conditions. For easier understanding, the best method is if we start with the simplest condition that means the least distracting circumstances. This can also be

The purpose of observing an area is to detect the unrequired event or incident as soon as possible. In general, the faster the autonomous system detects the event, the more effective it is to apply. We need to look at how to optimize the path planning of

The purpose of path planning is to find the best route according to the desired

*A* → *B*(*s* ⇒ min;*t* ⇒ min) (1)

*Path planning between points of "A" and "B" in ideal (left) and in natural (right) circumstances with only one* 

The simplest assumption in reality is very rarely found. In most cases the natural conditions make the simplest approach impossible, which means longer paths as shown in **Figure 1** (right) and longer access times. If the ideal path between the two points is not available, you have to choose from the other options available. The number of available options may vary between zero and infinity, but both lower and upper extremes should be excluded. At the theoretical starting point, the zero option means that there is no point in the task, and with the infinite possibility, we can only count on the theory. By excluding the two extremes, we find that the number of solutions varies from 1 to a large number. The only possible path, of course, does not give a choice. The first choice appears in case of two different paths

target function between two points. The target function may have different expectations, such as making the route as short as possible or as fast as possible (1). Assuming a two-dimensional plane area and ignoring any kind of disturbing circumstance, ideally shown in **Figure 1** (left) and assuming constant speed, it

the autonomous system with flexible remote sensing methods.

means in both cases the same path and the same time spent:

**2.1 Path planning problems between two points**

**102**

**Figure 1.**

*option.*

**Figure 2.** *Path planning options between points of "A and "B" with two different possible routes.*

as shown in **Figure 2**. The quality of the different routes may be the same or different, but it is natural the better road quality allows faster progress, which means that it takes less time to do the same route length.

However, in case of different routes, choice is useless if there is no difference between them according to the target functions. The following options are available for two routes based on their length and quality:


In general, the last one can be assumed. This gives new more opportunities, so the quality of the longer road can be better or worse than the shorter one and vice versa. In the latter case, when a longer road is combined with a poorer quality, it is clear this is not a choice. In the first case, when the quality of the longer road is better than the shorter one, you can get the following solutions:


The above is a mere combination of two different routes. It is easy to notice that changing the conditions makes the above more complicated. Example, if we increase the optional routes or the possibility of road quality per each new route but even with changing the quality along one route, the solutions increase exponentially. It is easy to notice that the above assumptions provide an ever-increasing choice, which is in the direction of infinity. However, a large part of the choices can be excluded, so all of those are certainly in a less favorable direction than the one that has already been examined before. As an example, all new routes with the same or worse route quality compared to a route of a given length can be excluded if they are longer than the examined one.

**Figure 3.**

*An example for path planning between points of "A" and "B" in case of more options with pathway and with intermediate points.*

Based on the above, it can be observed that in natural conditions there can be a significant number of solutions even between two points.

#### **2.2 Path planning problems between several points**

If we assume more than two points to be touched in the course of the route, we find that the number of options increases dramatically again as shown in **Figure 3**. Optimizing a multipoint path planning in a given plane area raises the travelling salesman problem (TSP) that has already been examined by many studies. At elementary level this question is raised hundreds years ago together with the trade development; however, as a classic scientific problem, it was mentioned firstly by Held and Karp [7] and Bellman [8]. They used dynamic programming approaches to find the solution.

Later other researchers followed these methods [9, 10], and others developed new ones offering other algorithms as well as time-dependent TSP [11] or TSP with time window and precedence constraints [12].

As new technologies appear in autonomous systems, like unmanned aerial vehicles (UAV) or drone applications, researchers found new problems and tried to give new approaches finding the best or optimized solution. Some of these studies focus only on the drone applications; others tried to combine drone application with the traditional delivery system [13, 14]. In these studies authors used different examining methods, as well as exact methods [15], heuristic methods [16–18], or approximation algorithm [14]. Bouman et al. cites a detailed summary about the above researches and results [19].

Based on the above, TSP is a very complex therefore not just natural condition, but also some idealistic assumption can generate a significant number of solutions.
