Pareto optimal synthesis of eight-bar mechanism using meta-heuristic multi-objective search approaches: application to bipedal gait generation

Villarreal-Cervantes, Miguel Gabriel; Pantoja-García, Jesus Said; Rodríguez-Molina, Alejandro; Benitez-Garcia, Saul Enrique

doi:10.1080/00207721.2020.1837991

Cited by 10 publications

(8 citation statements)

References 53 publications

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“…Sa-ngiamvibool applied an optimal fuzzy-PID controller for hydrothermal systems [17]. Barik et al [18] used a fuzzy proportional, derivative integral controller to investigate the frequency fluctuations due to wind and solar-thermal based renewable power [19]. Acharya and Das [20] introduced a fuzzy-PID controller to enhance the pressure tracking profile of pressure-controlled ventilators [16].…”

Section: Literature Reviewmentioning

confidence: 99%

Optimal Fuzzy Proportional-Integral-Derivative Control for a Class of Fourth-Order Nonlinear Systems using Imperialist Competitive Algorithms

et al. 2022

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The proportional integral derivative (PID) controller has gained wide acceptance and use as the most useful control approach in the industry. However, the PID controller lacks robustness to uncertainties and stability under disturbances. To address this problem, this paper proposes an optimal fuzzy-PID technique for a two-degree-of-freedom cart-pole system. Fuzzy rules can be combined with controllers such as PID to tune their coefficients and allow the controller to deliver substantially improved performance. To achieve this, the fuzzy logic method is applied in conjunction with the PID approach to provide essential control inputs and improve the control algorithm efficiency. The achieved control gains are then optimized via the imperialist competitive algorithm. Consequently, the objective function for the cart-pole system is regarded as the summation of the displacement error of the cart, the angular error of the pole, and the control force. This control concept has been tested via simulation and experimental validations. Obtained results are presented to confirm the accuracy and efficiency of the suggested method.

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Section: Literature Reviewmentioning

confidence: 99%

Optimal Fuzzy Proportional-Integral-Derivative Control for a Class of Fourth-Order Nonlinear Systems using Imperialist Competitive Algorithms

et al. 2022

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“…So, the constraint given in ( 22) is included to guarantee the kinematic motion. This constraint is considered a hard one [33], and this must be evaluated before the computation of the objective function. Whether the constraint is not feasible, the objective function will take a very high value without continuing its evaluation.…”

Section: ) Objective Functionmentioning

confidence: 99%

“…The precision points are presented in (50). (3,37), (10,41), (17,41), (26,39), (28,33), (29,26), (26,23), (17,23), (11,24), (6,27), (0, 31)][mm]…”

Section: E Study Case 5: Twenty Precision Pointsmentioning

confidence: 99%

Optimum Synthesis of Four-Bar Mechanism by Using Relative Angle Method: A Comparative Performance Study

Valencia-Segura

Villarreal-Cervantes²,

Corona-Ramirez

et al. 2021

IEEE Access

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In this paper, the dimensional synthesis of the four-bar mechanism for path generation is formulated using the relative angle motion analysis and the link geometry parameterization with Cartesian coordinates. The Optimum Dimensional Synthesis using Relative Angles and the Cartesian space link Parameterization (ODSRA+CP) is stated as an optimization problem, and the solution is given by the differential evolution variant DE/best/1/bin. This study investigates the behavior and performance of such formulation and performs a comparative empirical study with the well-known synthesis method based on vector-loop equation motion analysis where different modifications in the metaheuristic algorithms are established in the literature to improve the obtained solution. Five study cases of dimensional synthesis for path generation with and without prescribed timing are solved and analyzed. The empirical results show that the way of stating the optimization problem in the ODSRA+CP significantly improves the search process for finding promising solutions in the optimizer without requiring algorithm modifications. Therefore, it is confirmed that the optimizer search process in the optimal synthesis of mechanisms is not the only way of improving the obtained solutions, but also the optimization problem formulation has a significant influence on the search for better solutions.INDEX TERMS Mechanism synthesis, four-bar mechanism, optimization, differential evolution.

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“…The second research trend studies the optimization-based structural design of bipedal systems, where the problem of finding the optimal structure parameters for different types of walking systems was proposed. For instance, in the design of the passive bipedal walker leg that performs limit cycles in both the frontal and sagittal planes [14], in the design of an eight-bar mechanism to fulfill the desired locomotion task with a minimum force transmission during the stance phase [15,16], in the design of Stephenson III six-bar mechanism for tracking of a gait trajectory [17] and in the optimal mass distribution for passive dynamic biped robot [18]. Although both research trends have shown their own advantages, the trade-off between the natural dynamics of the structure and the control signal features related to the walking performance has not been addressed.…”

Section: Introductionmentioning

confidence: 99%

Integrated Structure-Control Design of a Bipedal Robot Based on Passive Dynamic Walking

Martinez-Castelan

Villarreal-Cervantes

2021

Mathematics

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The design of bipedal robots is generally fulfilled through considering a sequential design approach, where a synergistic relationship between its structure and control features is not promoted. Hence, a novel integrated structure-control design approach is proposed to simultaneously obtain the optimal structural description, the torque magnitudes, and the on/off time intervals for the control signal input of a semi-passive bipedal robot. The proposed approach takes advantage of the natural dynamics of the system and the control signal activation/deactivation for generating stable gait cycles with minimum energy consumption. Consequently, the passive features of the semi-passive bipedal robot are included in the integrated structure-control design process through evaluating the system behavior along consecutive passive and semi-passive walking stages. Then, the proposed design approach is formulated as a nonlinear discontinuous dynamic optimization problem, where the solution search is carried out using the differential evolution algorithm due to the discontinuities of the semi-passive bipedal robot dynamics. The results of the proposal are compared with those obtained by a sequential design process. The integrated structure-control design achieves a reduction of 63.55% in the value of the performance function related to the synergy between the walking capability and energetic efficiency, with a reduction in the activation of the control and its magnitude of 95.41%.

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Pareto optimal synthesis of eight-bar mechanism using meta-heuristic multi-objective search approaches: application to bipedal gait generation

Cited by 10 publications

References 53 publications

Optimal Fuzzy Proportional-Integral-Derivative Control for a Class of Fourth-Order Nonlinear Systems using Imperialist Competitive Algorithms

Optimal Fuzzy Proportional-Integral-Derivative Control for a Class of Fourth-Order Nonlinear Systems using Imperialist Competitive Algorithms

Optimum Synthesis of Four-Bar Mechanism by Using Relative Angle Method: A Comparative Performance Study

Integrated Structure-Control Design of a Bipedal Robot Based on Passive Dynamic Walking

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