Abstract
The easy gait stability of biped robot is an important issue and has been mentioned in different works in literature. To evaluate the walking stability, we performed zero moment point (ZMP) analysis for the obtained trajectory model. Whale Optimization Algorithm (WOA) has been gained more interest, due to the fewer number of control parameters, and easy implementation of the code. However, WOA has low convergence speed and accuracy. In this paper, a new variant of WOA which focuses on balancing between exploration and exploitation is proposed. The proposed algorithm named as the A-C parametric WOA targets the A and C parameters of the standard WOA specifically through variation of "a" parameter non-linearly and randomly, as well as updating parameter "C" by applying inertia weight strategy. To verify the performance of the proposed A-C parametric WOA, we at first test it against the standard WOA using 41 benchmark functions from CEC'2005 and CEC'2017. The results show a success rate of 38 out of 41 functions, while the T-test and Wilcoxon analyses succeeded in 33 and 37 out of 41 respectively. Secondly, a comparative study has been held between the A-C parametric WOA and the most well-known state-of-art soft computing techniques (PSO, DE, CS, GWO, WOA, and AGWO) through the standard deviation (STD) and the average resulting in a success rate of 6 out of 8 common benchmark functions. Thirdly, the parametric A-C WOA is applied on a biped robot to find the optimal settings of the hip parameters that make ZMP stays in the middle of the support polygon as much as possible. A comparative study has been held between the proposed algorithm and various well-known algorithms (PSO, DE, GA, WOA, and SSA) resulting in the best convergence characteristic with a reduction in STD of 47.9% compared to the standard WOA. Results show that the proposed A-C parametric WOA has the best results with the lowest STD and minimum error. (C) 2018 Elsevier B.V. All rights reserved.