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Pareto design of state feedback tracking control of a biped robot via multiobjective PSO in comparison with sigma method and genetic algorithms: modified NSGAII and MATLAB's toolbox.

Mahmoodabadi MJ, Taherkhorsandi M, Bagheri A - ScientificWorldJournal (2014)

Bottom Line: An optimal robust state feedback tracking controller is introduced to control a biped robot.Three points are chosen from the nondominated solutions of the obtained Pareto front based on two conflicting objective functions, that is, the normalized summation of angle errors and normalized summation of control effort.Obtained results elucidate the efficiency of the proposed controller in order to control a biped robot.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, Iran.

ABSTRACT
An optimal robust state feedback tracking controller is introduced to control a biped robot. In the literature, the parameters of the controller are usually determined by a tedious trial and error process. To eliminate this process and design the parameters of the proposed controller, the multiobjective evolutionary algorithms, that is, the proposed method, modified NSGAII, Sigma method, and MATLAB's Toolbox MOGA, are employed in this study. Among the used evolutionary optimization algorithms to design the controller for biped robots, the proposed method operates better in the aspect of designing the controller since it provides ample opportunities for designers to choose the most appropriate point based upon the design criteria. Three points are chosen from the nondominated solutions of the obtained Pareto front based on two conflicting objective functions, that is, the normalized summation of angle errors and normalized summation of control effort. Obtained results elucidate the efficiency of the proposed controller in order to control a biped robot.

Show MeSH
The obtained Pareto fronts by using Sigma method [43], modified NSGAII [52], MATLAB's Toolbox MOGA, and the proposed algorithm regarding the optimal control design of the biped robot.
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Related In: Results  -  Collection


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fig2: The obtained Pareto fronts by using Sigma method [43], modified NSGAII [52], MATLAB's Toolbox MOGA, and the proposed algorithm regarding the optimal control design of the biped robot.

Mentions: The proposed method is used to find the proper state feedback parameters and remove the tedious and repetitive trial and error process. Furthermore, the results are compared with three prominent algorithms. The performance of a controlled closed loop system is usually assessed by a variety of goals [62]. In this study, the normalized summation of angles errors and normalized summation of control effort are regarded as the objective functions. These objective functions are minimized at the same time. The vector [K1, K2, K3, K1′, K2′, K3′] is the vector of selective parameters of state feedback control. These are positive constants. The normalized summation of angles errors and normalized summation of control effort are functions of this vector's components. In this regard, by choosing various amounts of the selective parameters, changes occur in the normalized summation of angles errors and normalized summation of control effort. This is an optimization problem with two objective functions (the normalized summation of angles errors and normalized summation of control effort) and six decision variables (K1, K2, K3, K1′, K2′, K3′). The regions of the selective parameters are(8)−200<K1,  K2′<0,  −10000<K2<−5000,−200<K3<−100,  −10000<K1′<−4000,−1000<K3′<−10.The feasibility and efficiency of the proposed multi-objective algorithm are assessed in comparison with Sigma method [23], modified NSGAII [41], and MATLAB Toolbox MOGA. The Pareto front of this multi-objective problem is shown in Figure 2. The swarm size is 10 and the maximum iteration equals 500. The term is limited to the range [−vave, +vave] in which vave = (xmax⁡ − xmin⁡)/2. While the velocity violates this range, it will be multiplied by a random number between [0,1]. Econstant   and Rneighborhood   are set at 25 and 0.02, respectively. Over iteration, the inertia weight W is linearly decreased from W1 = 0.9 to W2 = 0.4, C1 is linearly decreased from C1i = 2.5 to C1f = 0.5, and C2 is linearly increased from C2i = 0.5 to C2f = 2.5.


Pareto design of state feedback tracking control of a biped robot via multiobjective PSO in comparison with sigma method and genetic algorithms: modified NSGAII and MATLAB's toolbox.

Mahmoodabadi MJ, Taherkhorsandi M, Bagheri A - ScientificWorldJournal (2014)

The obtained Pareto fronts by using Sigma method [43], modified NSGAII [52], MATLAB's Toolbox MOGA, and the proposed algorithm regarding the optimal control design of the biped robot.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3927564&req=5

fig2: The obtained Pareto fronts by using Sigma method [43], modified NSGAII [52], MATLAB's Toolbox MOGA, and the proposed algorithm regarding the optimal control design of the biped robot.
Mentions: The proposed method is used to find the proper state feedback parameters and remove the tedious and repetitive trial and error process. Furthermore, the results are compared with three prominent algorithms. The performance of a controlled closed loop system is usually assessed by a variety of goals [62]. In this study, the normalized summation of angles errors and normalized summation of control effort are regarded as the objective functions. These objective functions are minimized at the same time. The vector [K1, K2, K3, K1′, K2′, K3′] is the vector of selective parameters of state feedback control. These are positive constants. The normalized summation of angles errors and normalized summation of control effort are functions of this vector's components. In this regard, by choosing various amounts of the selective parameters, changes occur in the normalized summation of angles errors and normalized summation of control effort. This is an optimization problem with two objective functions (the normalized summation of angles errors and normalized summation of control effort) and six decision variables (K1, K2, K3, K1′, K2′, K3′). The regions of the selective parameters are(8)−200<K1,  K2′<0,  −10000<K2<−5000,−200<K3<−100,  −10000<K1′<−4000,−1000<K3′<−10.The feasibility and efficiency of the proposed multi-objective algorithm are assessed in comparison with Sigma method [23], modified NSGAII [41], and MATLAB Toolbox MOGA. The Pareto front of this multi-objective problem is shown in Figure 2. The swarm size is 10 and the maximum iteration equals 500. The term is limited to the range [−vave, +vave] in which vave = (xmax⁡ − xmin⁡)/2. While the velocity violates this range, it will be multiplied by a random number between [0,1]. Econstant   and Rneighborhood   are set at 25 and 0.02, respectively. Over iteration, the inertia weight W is linearly decreased from W1 = 0.9 to W2 = 0.4, C1 is linearly decreased from C1i = 2.5 to C1f = 0.5, and C2 is linearly increased from C2i = 0.5 to C2f = 2.5.

Bottom Line: An optimal robust state feedback tracking controller is introduced to control a biped robot.Three points are chosen from the nondominated solutions of the obtained Pareto front based on two conflicting objective functions, that is, the normalized summation of angle errors and normalized summation of control effort.Obtained results elucidate the efficiency of the proposed controller in order to control a biped robot.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, Iran.

ABSTRACT
An optimal robust state feedback tracking controller is introduced to control a biped robot. In the literature, the parameters of the controller are usually determined by a tedious trial and error process. To eliminate this process and design the parameters of the proposed controller, the multiobjective evolutionary algorithms, that is, the proposed method, modified NSGAII, Sigma method, and MATLAB's Toolbox MOGA, are employed in this study. Among the used evolutionary optimization algorithms to design the controller for biped robots, the proposed method operates better in the aspect of designing the controller since it provides ample opportunities for designers to choose the most appropriate point based upon the design criteria. Three points are chosen from the nondominated solutions of the obtained Pareto front based on two conflicting objective functions, that is, the normalized summation of angle errors and normalized summation of control effort. Obtained results elucidate the efficiency of the proposed controller in order to control a biped robot.

Show MeSH