genetic algorithm optimization

This paper is concerned with fuzzy tracking control optimized via multi-objective particle swarm optimization for stable walking of biped robots. To present an optimal control approach, multi-objective particle swarm optimization is used to design the parameters of the control method     in comparison to three effectual multi-objective optimization algorithms in the literature. In particle swarm optimization, a dynamic elimination technique is utilized as a novel approach to prune the archive effectively. Moreover, a turbulence operator is used to skip the local optima and the personal best position of each particle is determined by making use of the Sigma method. Normalized summation of angles errors and normalized summation of control efforts are two conflicting objective functions addressed by dint of multi-objective optimization algorithms in the present investigation. By contrasting the Pareto front of multi-objective particle swarm optimization with the Pareto fronts of other methods, it is illustrated that multi-objective particle swarm optimization performs with high accuracy, convergence and diversity of solutions in the design of fuzzy tracking control for nonlinear dynamics of biped robots. Finally,  the proper performance of the proposed controller is demonstrated by the results presenting   an appropriate tracking system and optimal control inputs. Indeed, the appropriate tracking system   and optimal control inputs prove the efficiency of optimal fuzzy tracking control in dealing with the nonlinear dynamics of biped robots.