Pareto optimal design of a fuzzy adaptive sliding mode controller for a three-link model of a biped robot via the multi-objective improved team game algorithm

• Published in: Journal of the Brazilian Society of Mechanical Sciences and Engineering 2022-09, Vol.44 (9), Article 428
• Main Authors: Abedzadeh Maafi, Rahmat, Etemadi Haghighi, Shahram, Mahmoodabadi, Mohammad Javad
• Format: Article
• Language: English
• Subjects: Adaptive control; Algorithms; Control systems design; Controllers; Design optimization; Engineering; Fuzzy control; Fuzzy systems; Game theory; Mechanical Engineering; Multiple objective analysis; Nonlinear systems; Optimization algorithms; Pareto optimization; Pareto optimum; Robots; Sliding mode control; Technical Paper; Tracking control; Trajectory control
• ISSN: 1678-5878; 1806-3691
• DOI: 10.1007/s40430-022-03719-0

The control problem of a biped robot is scientifically challenging work because it is an unstable, multi-input–multi-output and extremely nonlinear system. This investigation tends to introduce Pareto optimal design of a fuzzy adaptive sliding mode control (FASMC) for the trajectory tracking control of a three-link model of a biped robot walking in the lateral plane on a slope utilizing a novel multi-objective optimization algorithm. In pursuance of this intention, at first, new adaption laws are presented to renovate sliding mode control coefficients by generalizing the gradient descent method. Afterward, a tuning methodology via suitable fuzzy systems is established to accurately adjust the control gains. Next, a new multi-objective optimization algorithm is exerted to ameliorate the performance of the designed controller. This optimization algorithm is an improved version of the team game algorithm for benefiting the advantages of new effective operators, non-dominated Pareto solution scheme, sigma method and dynamic elimination technique. To evaluate the competencies of this approach, its optimal solutions are compared with those of five outstanding algorithms on four standard test functions. Results authenticate that the suggested algorithm yields closer non-dominated Pareto solutions to the true optimal Pareto front in comparison with the results found by other techniques. Ultimately, by selecting three conflicting objective functions, the multi-objective optimization of the FASMC for the regarded biped robot is accomplished. Simulation results demonstrate that the presented strategy can meticulously converge the real tracking trajectories to the desired time-varying trajectories and achieve superior responses in comparison with the prior studies.