Multi-Objective Optimization of a Multi-Link Slider–Crank Mechanism for Vertical Motion Generation in Legged Robots
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Abstract
This study presents the design of a multi-link slider–crank mechanism for generating vertical motion in legged robots. The design problem is formulated as a problem of multi-objective optimization (MOO) with two primary objectives: (1) maximizing the vertical motion range to cover a specified target interval, and (2) minimizing horizontal deviation of the center of mass during motion. To prevent bias toward oversized mechanisms, the total link length is incorporated into the formulation. The MOO employs the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to obtain Pareto optimal solutions. NSGA-II yields 508 Pareto-optimal solutions, notably, 40.35% of the solutions achieve horizontal deviation below 1 mm. Compared to single-objective optimization (SOO), a specific solution obtained from the MOO solution set achieved a reduction in total link length of over 30% while maintaining high vertical motion efficiency and low horizontal deviation. Consequently, the solutions obtained from MOO offer more compact mechanisms than those from SOO. These findings highlight the effectiveness of the MOO framework in providing design flexibility and practical suitability for implementation in mobile robotic systems.
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