**5. Problem 2 of robot route optimization under limitations on risk of "failure" in conditions of uncertainties**

For a robot, the concept of "failure" under uncertainty is defined as the "unsuccess" to achieve the goal within a given time. It is assumed that there are several possible routes to achieve the goal, and uncertainties may include both the conditions for robot operation (including random events in orientation, localization, and mapping in cooperation with drone for gathering actual data). The minimum risk of failure under the existing conditions and limitations is used as a criterion of optimization.

The next four steps are proposed for cognitive solving of problem 2 of robot route optimization under limitations on risk of "failure" in conditions of uncertainties, see **Figure 9**.

**Step 1**. The complete set of route variants to achieve the goal within the given time, and for each variant—a set of components is defined (redefined). Data characterizing every part of route for each of the variants are gathered (refined) for

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

**Figure 9.** *Steps for cognitive solving of problem 2.*

1.on the stages of system concept, development, production, and support: system parameters, software, technical, and management measures (Q) are the most rationale for the given period if on them the minimum of expenses

Q

at limitations on probability of an admissible level of quality *P*quality (Q) ≥ *P*adm. and expenses for operation Сoper. (Q) ≤ Сadm. and under other development, oper-

2.on utilization stage: system parameters, software, technical, and management measures (Q) are the most rational for the given period of operation if on them the maximum of probability of correct system operation is reached

Q

at limitations on probability of an admissible level of quality *P*quality (Q) ≥ *P*adm. and expenses for operation Сoper. (Q) ≤ С adm. and under other operation or main-

These statements (6), (7) may be transformed into the problems of expenses or risk minimization in different limitations. There may be a combination of these

**Step 4**. A plan for the optimal variant of actions (defined in Step 3) is formed. To support the efficiency and/or effectiveness of the functions, the achievable gain calculated at Step 3 is recorded. New knowledge is improved, accumulated, and systematized in K-base by comparing it with reality (for example, by a specific

Note. A solution that meets all conditions may not exist. In this case, there is no optimal variant of planning the possibilities of functions performance on the base of monitored information. Additional systems analysis, adjustment of the criteria, or

**5. Problem 2 of robot route optimization under limitations on risk of**

For a robot, the concept of "failure" under uncertainty is defined as the "unsuccess" to achieve the goal within a given time. It is assumed that there are several possible routes to achieve the goal, and uncertainties may include both the conditions for robot operation (including random events in orientation, localization, and mapping in cooperation with drone for gathering actual data). The minimum risk of failure under the existing conditions and limitations is used as a

The next four steps are proposed for cognitive solving of problem 2 of robot route optimization under limitations on risk of "failure" in conditions of uncer-

**Step 1**. The complete set of route variants to achieve the goal within the given time, and for each variant—a set of components is defined (redefined). Data characterizing every part of route for each of the variants are gathered (refined) for

For limitation on *P*quality (Q) K-base is used; for example, see **Table 1**. For calculation probabilistic measures for given prognostic period, the proposed models

Zdev*:* ð Þ Q , (6)

*P*quality ð Þ Q , (7)

Zdev*:* Qrational ð Þ¼ min

*P*quality Qrational ð Þ¼ max

(Zdev.) for creation of system is reached

ation, or maintenance conditions;

*Probability, Combinatorics and Control*

formal statements in system's life cycle.

method considering AIS capabilities for self-improving).

**"failure" in conditions of uncertainties**

criterion of optimization.

tainties, see **Figure 9**.

**16**

limitations is required (see, for example, ISO/IEC/IEEE 15288).

tenance conditions.

are used.

modeling. To do this, the robot can use data from various sources (for example, from air drones, intelligent buoys on the water or sensors under water, etc.). If necessary, possible damages are taken into account. For example, each use case may be characterized by an expected damage in comparable conventional units. If the objective value of a damage cannot be defined, expert value of expected level of "failure" for each variant may be established, for example, on a dimensionless scale from 0 to 100 (0—"no damages", i.e., "success"; 100—"the maximal damage"). After learning by K-base, self-improving AIS also uses input and the corresponding results of probabilistic modeling in a form of the solution of previously specific encountered problem 2.

The index i of the first part of the selected route is set to the initial value i = 1.

**Step 2**. The accumulated knowledge is used to refine the input for prognostic modeling. A quality of used information is estimated by models above considering limitations from **Table 1**. Using probabilistic model, a calculation of the probability of failure is carried out for each variant. From the set of remaining route variants, the optimal one is chosen (for it is the minimum probability of failure that is achieved).

**Step 3**. The robot overcomes the i-th part of the selected route. If the part cannot be overcome successfully according to probabilistic modeling and/or actual data, the comeback to the initial point of the part is being. If an alternative route is not here, the comeback to initial point of the previous part is being. The input for modeling every part of possible route for each of the variants is updated. New knowledge is improved, accumulated, and systematized in K-base by comparing it with reality (using a specific method considering AIS capabilities for self-improving).

**Step 4**. If, after overcoming the i-th part, the robot arrived at the intended point of route (i.e., the last part of the route is overcome and the goal is achieved), then the solution of task 2 for optimizing the route is complete. If the robot has not yet arrived at the intended point (i.e., the last part of the route is not overcome), then

the complete set of different route variants for achieving the goal is redefined (similar to step 1). The input for modeling every part of possible route for each of the variants is updated. i = i + 1. Then, Steps 2–4 are repeated until the last part of the route is overcome on the set of possible variants (i.e., it means the goal is achieved and problem 2 is solved).

If the set of possible options is exhausted and the goal is not achieved, it is concluded that the goal is unattainable with the risk of "failure" less than the acceptable risk (i.e., it means an impossibility of solving problem 2 in the defined conditions).

Thus, for optimizing robot route in space (i.e., for the "successful" solution of problem 2) in real time, information gathering, probabilistic predictions for possible route variants, their comparison, the choice of the best variant, the implementation of further actions, the improvement, accumulation, systematization, and use of knowledge are being, see **Figure 9**.

Note. The proposed methods of solving problems 1 and 2 are essentially identical approaches based on the use of the same probabilistic models (Section 3). The only difference is that for the system planning the possibilities of functions performance (problem 1), the concept of "success" is used; and for the robot route optimization under limitations on risk of "failure" (problem 2), the concept of "failure," which is defined as the lack of "success," is used.

Results of modeling the first variant of project have shown the following (**Figure 10**): for operator's console (first subsystem), power unit (second subsystem) and central controller with a handle of control (third subsystem) MTBLI = 8766 h, for manipulator means (including a hinge of roving of key, a hinge of shoulder, a hinge of roving of elbow, a hinge of elbow, a hinge of roving of brush, a hinge of brushes, a hinge of brush rotation, a device for grasping, videocamera—united as subsystem 4, which can operate if one of these means is available) MTBLI = 31,293 h, for all complex 1,…,4 MTBLI = 2672 h; probability of reliable operation of complex 1,…,4 during 8 h is equal to 0.979; probability of

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

The maximum probability of "success" and minimum risk of "failure" under

The results of first variant are used for estimating input for the second variant of modeling: every subsystem for second variant (for subsystems equipped by AIS) is characterized by MTBLI = 31,293 h in analogy to the subsystem 4 of first variant. Owing to AIS, the frequency of anomalies is about 0.28 year<sup>1</sup> (it is equal to 1/MTBLI), but the conditions of anomalies activation time are more strong: the mean time is 30 min. The time between the end of diagnostics and the beginning of

Analysis of modeling results proves: risks are very high despite the use of AIS

For a robot-manipulator used in space, new knowledge for accumulating and

1.The input (used for modeling) characterizes inadmissible conditions for

2.The probability of "success" on level 0.98 or risk of "failure" on level 0.02 during six sessions of cosmonaut work is inadmissible for reliable robot-

3.For a robot-manipulator used in space, the level 31,293 h of MTBLI is inadmissible level for every compound subsystem equipped by

limitations on the successful functions performance are used as a criterion.

the next diagnostics is 1 month, and the recovery time is about 1 day. What about the risks of "failure" during period from 0.05 to 2 years?

with the described characteristics, see **Figure 11**.

*Results of probabilistic modeling robot-manipulator operation.*

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

functions performance by robot-manipulator.

manipulator operation more than 1–2 weeks in space.

improving K-base is as follows:

**Figure 10.**

considered AIS.

**19**

reliable operation of complex 1,…,4 during 48 h is equal to 0.965.
