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Reduction of Logical-Probabilistic and Logical-Linguistic Constraints to Interval Constraints in the Synthesis of Optimal SEMS

  • Andrey E. Gorodetskiy
  • Irina L. Tarasova
  • Vugar G. Kurbanov
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 174)

Abstract

Problem statement: modern dynamic robotic systems, such as SEMS, contain high-precision information-measuring and control systems (IMCS). The analysis and synthesis of such IMCS usually relies on structural identification techniques and computational optimization techniques. A feature of SEMS is the use of such systems in the contours of “non-rigid” models, whose structure, parameters and state vector are not specified at the design stage, but are in real time when they operate. This greatly complicates the synthesis of SEMS, especially when limiting the speed of microprocessor controls. In this case, an approach called the method of recurrent target inequalities (RTI) and based on the search for suboptimal solutions and reduction of the original problem of synthesis to the search for the target set described by systems of inequalities, including dynamic ones, can be used. The need to select the best trajectories (scenarios of SEMS dynamics) in conditions of incomplete certainty requires taking into account the limitations of the environment of functioning which are introduced in the form of logical-probabilistic and/or logical-linguistic expressions. Therefore, this approach to the synthesis of SEMS to date has not been developed. However, the relevance of research in the direction of the development of the RTI method for the synthesis of SEMS is undeniable. In particular, the development of the RTSN method is closely related to the solution of the problem of reducing logical-probabilistic and logical-linguistic constraints to interval constraints. Purpose of research: solution of the problem of reduction of logical-probabilistic and logical-linguistic constraints to interval constraints and demonstration of decision-making efficiency in conditions of not complete certainty on the example of the algorithm for finding optimal trajectories of motion. Results: a brief overview of approaches to the synthesis of intelligent robots type SEMS. The peculiarities of the use of the RTI method in the presence of restrictions from the environment of functioning in the form of logical-probabilistic and/or logical-linguistic expressions are analyzed. Theorems of data of logical-probabilistic and logical-linguistic expressions to interval are given. The algorithm of decision-making at logical-probabilistic and logical-linguistic restrictions is shown on the example of the algorithm of search of optimum trajectories of movement of the SEMS type robot. Practical significance: the proven theorems for reducing logical-probabilistic and logical-linguistic expressions to interval expressions can be effectively used in robot control planning systems that provide the choice of the best scenarios of movements in conditions of not complete certainty, as evidenced by the example.

Keywords

Robots SEMS Control planning Dynamic models The method of recurrent target inequalities Decision-making in conditions of uncertainty Logical-probabilistic and logical-linguistic constraints Theorems reducing constraints to interval 

Notes

Acknowledgements

This work was financially supported by Russian Foundation for Basic Research, Grant 16-29-04424 and Grant 18-01-00076.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Andrey E. Gorodetskiy
    • 1
  • Irina L. Tarasova
    • 1
    • 2
  • Vugar G. Kurbanov
    • 1
    • 3
  1. 1.Institute of Problems of Mechanical Engineering Russian Academy of Sciences, V.O.Saint-PetersburgRussia
  2. 2.Peter the Great St. Petersburg Polytechnic UniversitySaint-PetersburgRussia
  3. 3.Saint-Petersburg State University of Aerospace InstrumentationSaint-PetersburgRussia

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