Abstract
This paper is devoted to the problem of determining the workspace of robots. We consider an approach to the development of a numerical method for approximating the set of solutions of a system of nonlinear inequalities based on the concept of non-uniform coverings. An approach is proposed based on the transformation of non-uniform covering sets into a set of partially ordered sets of integers to reduce computational complexity. An algorithm for transforming boxes of a covering set is presented. The approach has been tested for a 3-RPS robot. The results of the mathematical simulation and analysis of the effectiveness of the proposed approach based on an estimate of the reduction in the amount of numbers describing the covering set are presented.
This work was supported by the Russian Science Foundation, the agreement number 16-19-00148.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Evtushenko, Y.G.: Numerical methods for finding global extrema (case of a non-uniform mesh). USSR Comput. Math. Math. Phys. 11(6), 38–54 (1971)
Kong, X., Gosselin, C.M.: Type Synthesis of Parallel Mechanisms, vol. 33. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71990-8
Merlet, J.P.: Parallel Robots, 2nd edn., pp. 269–285. Springer, Heidelberg (2007). https://doi.org/10.1007/1-4020-4133-0
Aleshin, A.K., Glazunov, V.A., Rashoyan, G.V., Shai, O.: Analysis of kinematic screws that determine the topology of singular zones of parallel-structure robots. J. Mach. Manuf. Reliab. 45(4), 291–296 (2016). https://doi.org/10.3103/S1052618816040026
Posypkin, M.: Automated robot’s workspace approximation. In: Journal of Physics: Conference Series, vol. 1163, no. 1, p. 012050. IOP Publishing (2019)
Evtushenko, Y., Posypkin, M., Rybak, L., Turkin, A.: Approximating a solution set of nonlinear inequalities. J. Global Optim. 71(1), 129–145 (2017). https://doi.org/10.1007/s10898-017-0576-z
Malyshev, D., Posypkin, M., Rybak, L., Usov, A.: Approaches to the determination of the working area of parallel robots and the analysis of their geometric characteristics. Eng. Trans. 67(3), 333–345 (2019)
Rybak, L.A., Behera, L., Malyshev, D.I., Virabyan, L.G.: Approximation of the workspace of parallel and serial structure manipulators as part of the multi-robot system. Bull. BSTU Named After V.G. Shukhov 8, 121–128 (2019)
Malyshev, D.I., Posypkin, M.A., Gorchakov, A.Y., Ignatov, A.D.: Parallel algorithm for approximating the work space of a robot. Int. J. Open Inf. Technol. 7(1), 1–7 (2019)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Rybak, L., Malyshev, D., Gaponenko, E. (2020). Optimization Algorithm for Approximating the Solutions Set of Nonlinear Inequalities Systems in the Problem of Determining the Robot Workspace. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Advances in Optimization and Applications. OPTIMA 2020. Communications in Computer and Information Science, vol 1340. Springer, Cham. https://doi.org/10.1007/978-3-030-65739-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-65739-0_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-65738-3
Online ISBN: 978-3-030-65739-0
eBook Packages: Computer ScienceComputer Science (R0)