Multi-Objective Optimization of the Chebyshev Lambda Mechanism

Abstract

Walking mechanisms are a solution for cases in which wheels are not applicable, such as uneven or stepped surfaces and surfaces with
obstacles. Furthermore, it is possible to tailor mechanism footpaths to expected working conditions through optimization. Thus, in this paper, a mechanism optimization process was proposed, focusing on single-leg performance. Numerical Simulink calculations were used to determine objective function values, which were then input to a non-dominated sorting genetic algorithm (NSGA-II) for optimization. In each following generation, NSGA-II provided a new set of units for evaluation. The procedure was applied to the single leg of the Chebyshev lambda mechanism to better illustrate it, enabling a comprehensive analysis of candidates. Four objective functions (i.e., length in the x-direction, trajectory height variation, maximum foot acceleration, and foot speed fluctuation) were used to carry out a multi-objective optimization. The calculation time was approximately 2 s/unit.