A solving tool for fuzzy quadratic optimal control problems

In this paper we propose an iterative method to solve an optimal control problem, with fuzzy target and constraints. The algorithm is developed in such a way as to satisfy the target function and the constraints. The algorithm can be applied only if a method exists to solve a crisp parametric sub-problem obtained by the original one. This is the case for a quadratic-linear target function with linear constraints, for which some well established solvable methods exist for the crisp associated sub-problem. A numerical test confirmed the good convergence properties.fuzzy, mathematical programming

Modelling an Industrial Robot and Its Impact on Productivity

[EN] This research aims to design an efficient algorithm leading to an improvement of productivity by posing a multi-objective optimization, in which both the time consumed to carry out scheduled tasks and the associated costs of the autonomous industrial system are minimized. The algorithm proposed models the kinematics and dynamics of the industrial robot, provides collision-free trajectories, allows to constrain the energy consumed and meets the physical characteristics of the robot (i.e., restriction on torque, jerks and power in all driving motors). Additionally, the trajectory tracking accuracy is improved using an adaptive fuzzy sliding mode control (AFSMC), which allows compensating for parametric uncertainties, bounded external disturbances and constraint uncertainties. Therefore, the system stability and robustness are enhanced; thus, overcoming some of the limitations of the traditional proportional-integral-derivative (PID) controllers. The trade-offs among the economic issues related to the assembly line and the optimal time trajectory of the desired motion are analyzed using Pareto fronts. The technique is tested in different examples for a six-degrees-of-freedom (DOF) robot system. Results have proved how the use of this methodology enhances the performance and reliability of assembly lines.Llopis-Albert, C.; Rubio Montoya, FJ.; Valero Chuliá, FJ. (2021). Modelling an Industrial Robot and Its Impact on Productivity. Mathematics. 9(7):1-13. https://doi.org/10.3390/math907076911397AOYAMA, T., NISHI, T., & ZHANG, G. (2017). Production planning problem with market impact under demand uncertainty. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 11(2), JAMDSM0019-JAMDSM0019. doi:10.1299/jamdsm.2017jamdsm0019Llopis-Albert, C., Rubio, F., & Valero, F. (2015). Improving productivity using a multi-objective optimization of robotic trajectory planning. Journal of Business Research, 68(7), 1429-1431. doi:10.1016/j.jbusres.2015.01.027Rubio, F., Valero, F., Sunyer, J., & Cuadrado, J. (2012). Optimal time trajectories for industrial robots with torque, power, jerk and energy consumed constraints. Industrial Robot: An International Journal, 39(1), 92-100. doi:10.1108/01439911211192538Llopis-Albert, C., Rubio, F., & Valero, F. (2018). Optimization approaches for robot trajectory planning. Multidisciplinary Journal for Education, Social and Technological Sciences, 5(1), 1. doi:10.4995/muse.2018.9867Yang, Y., Pan, J., & Wan, W. (2019). Survey of optimal motion planning. IET Cyber-Systems and Robotics, 1(1), 13-19. doi:10.1049/iet-csr.2018.0003Gasparetto, A., & Zanotto, V. (2008). A technique for time-jerk optimal planning of robot trajectories. Robotics and Computer-Integrated Manufacturing, 24(3), 415-426. doi:10.1016/j.rcim.2007.04.001Mohammed, A., Schmidt, B., Wang, L., & Gao, L. (2014). Minimizing Energy Consumption for Robot Arm Movement. Procedia CIRP, 25, 400-405. doi:10.1016/j.procir.2014.10.055Van den Berg, J., Abbeel, P., & Goldberg, K. (2011). LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information. The International Journal of Robotics Research, 30(7), 895-913. doi:10.1177/0278364911406562Liu, S., Sun, D., & Zhu, C. (2011). Coordinated Motion Planning for Multiple Mobile Robots Along Designed Paths With Formation Requirement. IEEE/ASME Transactions on Mechatronics, 16(6), 1021-1031. doi:10.1109/tmech.2010.2070843Plaku, E., Kavraki, L. E., & Vardi, M. Y. (2010). Motion Planning With Dynamics by a Synergistic Combination of Layers of Planning. IEEE Transactions on Robotics, 26(3), 469-482. doi:10.1109/tro.2010.2047820Rubio, F., Llopis-Albert, C., Valero, F., & Suñer, J. L. (2015). Assembly Line Productivity Assessment by Comparing Optimization-Simulation Algorithms of Trajectory Planning for Industrial Robots. Mathematical Problems in Engineering, 2015, 1-10. doi:10.1155/2015/931048Rubio, F., Llopis-Albert, C., Valero, F., & Suñer, J. L. (2016). Industrial robot efficient trajectory generation without collision through the evolution of the optimal trajectory. Robotics and Autonomous Systems, 86, 106-112. doi:10.1016/j.robot.2016.09.008Llopis-Albert, C., Valero, F., Mata, V., Pulloquinga, J. L., Zamora-Ortiz, P., & Escarabajal, R. J. (2020). Optimal Reconfiguration of a Parallel Robot for Forward Singularities Avoidance in Rehabilitation Therapies. A Comparison via Different Optimization Methods. Sustainability, 12(14), 5803. doi:10.3390/su12145803Llopis-Albert, C., Valero, F., Mata, V., Escarabajal, R. J., Zamora-Ortiz, P., & Pulloquinga, J. L. (2020). Optimal Reconfiguration of a Limited Parallel Robot for Forward Singularities Avoidance. Multidisciplinary Journal for Education, Social and Technological Sciences, 7(1), 113. doi:10.4995/muse.2020.13352Yang, J., Su, H., Li, Z., Ao, D., & Song, R. (2016). Adaptive control with a fuzzy tuner for cable-based rehabilitation robot. International Journal of Control, Automation and Systems, 14(3), 865-875. doi:10.1007/s12555-015-0049-4Zhang, G., & Zhang, X. (2016). Concise adaptive fuzzy control of nonlinearly parameterized and periodically time-varying systems via small gain theory. International Journal of Control, Automation and Systems, 14(4), 893-905. doi:10.1007/s12555-015-0054-7SUTONO, S. B., ABDUL-RASHID, S. H., AOYAMA, H., & TAHA, Z. (2016). Fuzzy-based Taguchi method for multi-response optimization of product form design in Kansei engineering: a case study on car form design. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 10(9), JAMDSM0108-JAMDSM0108. doi:10.1299/jamdsm.2016jamdsm0108DUBEY, A. K. (2009). Performance Optimization Control of ECH using Fuzzy Inference Application. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 3(1), 22-34. doi:10.1299/jamdsm.3.22Zhang, H., Fang, H., Zhang, D., Luo, X., & Zou, Q. (2020). Adaptive Fuzzy Sliding Mode Control for a 3-DOF Parallel Manipulator with Parameters Uncertainties. Complexity, 2020, 1-16. doi:10.1155/2020/2565316Markazi, A. H. D., Maadani, M., Zabihifar, S. H., & Doost-Mohammadi, N. (2018). Adaptive Fuzzy Sliding Mode Control of Under-actuated Nonlinear Systems. International Journal of Automation and Computing, 15(3), 364-376. doi:10.1007/s11633-017-1108-5Truong, H. V. A., Tran, D. T., To, X. D., Ahn, K. K., & Jin, M. (2019). Adaptive Fuzzy Backstepping Sliding Mode Control for a 3-DOF Hydraulic Manipulator with Nonlinear Disturbance Observer for Large Payload Variation. Applied Sciences, 9(16), 3290. doi:10.3390/app9163290Li, T.-H. S., & Huang, Y.-C. (2010). MIMO adaptive fuzzy terminal sliding-mode controller for robotic manipulators. Information Sciences, 180(23), 4641-4660. doi:10.1016/j.ins.2010.08.00

Approximating a similarity matrix by a latent class model: A reappraisal of additive fuzzy clustering

Let Q be a given n×n square symmetric matrix of nonnegative elements between 0 and 1, similarities. Fuzzy clustering results in fuzzy assignment of individuals to K clusters. In additive fuzzy clustering, the n×K fuzzy memberships matrix P is found by least-squares approximation of the off-diagonal elements of Q by inner products of rows of P. By contrast, kernelized fuzzy c-means is not least-squares and requires an additional fuzziness parameter. The aim is to popularize additive fuzzy clustering by interpreting it as a latent class model, whereby the elements of Q are modeled as the probability that two individuals share the same class on the basis of the assignment probability matrix P. Two new algorithms are provided, a brute force genetic algorithm (differential evolution) and an iterative row-wise quadratic programming algorithm of which the latter is the more effective. Simulations showed that (1) the method usually has a unique solution, except in special cases, (2) both algorithms reached this solution from random restarts and (3) the number of clusters can be well estimated by AIC. Additive fuzzy clustering is computationally efficient and combines attractive features of both the vector model and the cluster mode

On the interpretation and identification of dynamic Takagi-Sugenofuzzy models

Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples