**6.5 Example of robot route optimization under limitations on risk of "failure" in conditions of uncertainties**

Applicability of the proposed probabilistic methods and models is demonstrated to improve some of the existing capabilities of rescue robot for route optimization. This subsection contains an explanation on how problem 2 may be cognitively solved. Similar problems of specific robot route optimization from point A (Start) to point F (Finish) can arise on water, under water (**Figure 15**), in burning wood (**Figure 16**), in the conditions of a city or in mountains (**Figure 17**), and in other situations in conditions of uncertainties. Specific cases of uncertainties can be connected additionally with complex conditions of environment and necessity of robotics orientation, localization, and mapping that influences on input for the proposed probabilistic models.

Here, we demonstrate the proposed approach by a simplified example of moving a special rescue robot from point A to the final point F of the route (from where the SOS signals from tourists are following). It is required to optimize the route of the robot in space under uncertainty of weather, complex snow conditions in mountains to achieve the goal in 2 h with an acceptable risk of failure less than 0.1 (i.e., a probability of success should be more than 0.9). Interaction with the drone-

*A system view on situation for robot route from point A (Start) to point F (Finish) in mountains.*

*Probabilistic Methods for Cognitive Solving of Some Problems in Artificial Intelligence Systems*

The applications to cognitive solving the problem of robot route optimization

**Step 1**. The complete set of route variants to achieve the goal within about 2 h: first route is ABCF, second route AGKF, third route if AHLDEF, and fourth variant is a combination of routes 1–3. Points A, B, C, G, K, H, L, D, E, F mean that they may change the route (including return to the previous point). Respectively, it may be a refinement of the further route at these points. Robot speed allows to overcome

For each variant, a set of system compared by modeling is defined: there are ABCF, AGKF, AHLDEF, and possible combinations. Inputs characterizing every part of route for each of the variants are formed by K-base and gathered data from

• Frequencies of the occurrences of potential threats are for route ABCF σ = 1 time at 10 h, AGKF σ = 1.5 times at 10 h, AHLDEF σ = 2 times at 10 h (since

• Time between the end of diagnostics and the beginning of the next diagnostics

• Recovery time of robot availability = 10 min (for modified model [42–44])

informant is supposed, see **Figure 17**.

*DOI: http://dx.doi.org/10.5772/intechopen.89168*

are demonstrated by the next steps.

8.00 a.m. to 8.00 p.m.)

• Mean activation time of threats Tactiv = 30 min

• Diagnostics time of robot availability Tdiag = 30 s

of robot availability Tbetw. = 2 min

• Given prognostic period Tgiven =2h

any route in time.

**Figure 17.**

drone-informant:

**27**

#### **Figure 15.**

*A system view on situation for robot route from point A (Start) to point F (Finish) on water and under water.*

*Probabilistic Methods for Cognitive Solving of Some Problems in Artificial Intelligence Systems DOI: http://dx.doi.org/10.5772/intechopen.89168*

#### **Figure 17.**

4.Analyzed project of AISs operation effectiveness (that transform all system components to the level which is proper to medium-level workers of floating

**6.5 Example of robot route optimization under limitations on risk of "failure"**

Applicability of the proposed probabilistic methods and models is demonstrated to improve some of the existing capabilities of rescue robot for route optimization. This subsection contains an explanation on how problem 2 may be cognitively solved. Similar problems of specific robot route optimization from point A (Start) to point F (Finish) can arise on water, under water (**Figure 15**), in burning wood (**Figure 16**), in the conditions of a city or in mountains (**Figure 17**), and in other situations in conditions of uncertainties. Specific cases of uncertainties can be connected additionally with complex conditions of environment and necessity of robotics orientation, localization, and mapping that influences on input for the

*A system view on situation for robot route from point A (Start) to point F (Finish) on water and under water.*

*A system view on situation for robot route from point A (Start) to point F (Finish) in burning wood.*

oil and gas platform) can be added to K-base history as precedent.

**in conditions of uncertainties**

*Probability, Combinatorics and Control*

proposed probabilistic models.

**Figure 15.**

**Figure 16.**

**26**

*A system view on situation for robot route from point A (Start) to point F (Finish) in mountains.*

Here, we demonstrate the proposed approach by a simplified example of moving a special rescue robot from point A to the final point F of the route (from where the SOS signals from tourists are following). It is required to optimize the route of the robot in space under uncertainty of weather, complex snow conditions in mountains to achieve the goal in 2 h with an acceptable risk of failure less than 0.1 (i.e., a probability of success should be more than 0.9). Interaction with the droneinformant is supposed, see **Figure 17**.

The applications to cognitive solving the problem of robot route optimization are demonstrated by the next steps.

**Step 1**. The complete set of route variants to achieve the goal within about 2 h: first route is ABCF, second route AGKF, third route if AHLDEF, and fourth variant is a combination of routes 1–3. Points A, B, C, G, K, H, L, D, E, F mean that they may change the route (including return to the previous point). Respectively, it may be a refinement of the further route at these points. Robot speed allows to overcome any route in time.

For each variant, a set of system compared by modeling is defined: there are ABCF, AGKF, AHLDEF, and possible combinations. Inputs characterizing every part of route for each of the variants are formed by K-base and gathered data from drone-informant:


i = 1.

**Step 2** (i = 1). Using probabilistic model, a calculation of the probability of failure is carried out for each variant. From the set of variants ABCF, AGKF, and AHLDEF, the shorter variant ABCF for which risk is equal to 0.034 is chosen (for the route AGKF risk = 0.051, for route AHLDEF risk = 0.067), see **Figure 18**. The relevant data from the drone about the forecasted conditions and the weather on the part CF to 8.30 a.m. are taken into account.

**Step 4**. After overcoming the part GHLDEF, the robot arrived at the intended

*Probabilistic Methods for Cognitive Solving of Some Problems in Artificial Intelligence Systems*

Thus, the way ABCBGHLDEF is the result of optimization. The robot purpose was achieved owing to preventive measures which were defined by using risk

1.The input (used for modeling) characterizes possible complex conditions for rescue robot route optimization under limitations on risk of "failure" in conditions of uncertainties. In particular, the information updates every 2 min for robot route optimization under limitations on risk of "failure" less than 0.1

2.The acceptable risk 0.1 is justified; the predicted risks for all variants of the

The proposed approach to build and implement the probabilistic methods and

• The problem of planning the possibilities of functions performance on the base

• The problem of robot route optimization under limitations on risk of "failure"

There is proposed to carry out probabilistic prediction of critical processes in time so that not only to act according to the prediction, but also to compare pre-

The described analytical solutions are demonstrated by practical examples

Forming input for probabilistic modeling from monitored data

A cognitive solving of the chosen problems consists in improvements,

System planning the possibilities of functions performance in space by using robot-manipulators, by AIS for a coal company and for a floating oil and gas

Robot route optimization under limitations on risk of "failure" in conditions of

According to the proof of formula (1): because between diagnostics system is not protected from threats an influence (a loss of integrity) will take place only after danger occurrence and activation during given time before the next diagnostic (**Figure 6**). A risk to lose integrity (i.e., probability of "failure") is equal to

3.Analyzed project can be added to K-base history as precedent.

models is demonstrated by application to cognitive solving:

of monitored information about events and conditions

dictions against their coincidence to the subsequent realities.

accumulation, analysis, and use of appearing knowledge.

New knowledge for accumulating and improving K-base is as follows:

control on the way (with probability of "success" more than 0.9).

is admissible for considered situation.

routes did not exceed 0.1.

in conditions of uncertainties

**7. Conclusion**

such as:

platform

**Appendix**

**29**

uncertainties

Proofs for formulas (1)–(3)

point F of route in time.

*DOI: http://dx.doi.org/10.5772/intechopen.89168*

**Step 3** (i = 1). The robot overcomes the part AB of route. For the new initial point B, the input for modeling every part of possible route is updated in real time for routes BCF, BGKF, and BGHLDEF.

**Step 4** (i = 1). The robot has not yet arrived at the intended point F (i.e., the last part of the route is not overcome).

i = i + 1 = 2.

**Step 2** (i = 2 for variants BCF, BGKF, and BGHLDEF). Input for modeling is not changed. Risks are the same. From the route variants BCF, BGKF, and BGHLDEF, the shorter one BCF (with minimal risk) is chosen.

**Step 3** (i = 2 for variant BCDEF). The robot overcomes the part BC. For the new initial point C, the input for modeling every part of possible route is updated in real time: bad weather on the CF part does not allow further movement. And weather improvements in the next 2 h are not expected. Part CF is impassable. The comeback to the initial point B of the part is being.

**Step 2** (i = 2 for two remaining variants). From variants BGKF and BGHLDEF, the shorter one BGKF (with minimal risk 0.051) is chosen.

**Step 3** (i = 2 for variant BGKF). The robot overcomes the part BG. For the new initial point G, the input for modeling every part of possible route is updated in real time: according drone from 9.00 a.m. on parts GK and KF the imminent avalanche are detected. The accumulated knowledge is used to clarify the input for modeling, namely: the frequency threats in the part GKF increases from 1.5 to 2.5 times at 10 h. Using a probabilistic model for each variant, a recalculation of the risk of failure is carried out. Of the variants GKF and GHLDEF, the variant GHLDEF is chosen (risk is equal to 0.067, for the route GKF risk equals 0.083).

#### **Figure 18.**

*The risk of "failure" in dependence on prognostic period during the robot route from point A (Start) to point F (Finish).*

*Probabilistic Methods for Cognitive Solving of Some Problems in Artificial Intelligence Systems DOI: http://dx.doi.org/10.5772/intechopen.89168*

**Step 4**. After overcoming the part GHLDEF, the robot arrived at the intended point F of route in time.

Thus, the way ABCBGHLDEF is the result of optimization. The robot purpose was achieved owing to preventive measures which were defined by using risk control on the way (with probability of "success" more than 0.9).

New knowledge for accumulating and improving K-base is as follows:

