Hierarchical multi-objective optimization for precise performance design of closed-chain legged mechanisms

• Hierarchical Multi-Objective Optimization for Legged Mechanisms. • Numerical approach for switching bench into walking trajectory. • Optimization strategy with and without trajectory shape constraints. • Reproduce compound cycloid trajectory by closed-chain legs for the first time. • Optimal design strategy for topological reconfigurable legged mechanisms. Over the past decades, the performance design of closed-chain legged mechanisms (CLMs) has not been adequately addressed. Most existing design methodologies have predominantly relied on trajectory synthesis, which inadvertently prioritizes less critical performance aspects. This study proposes a hierarchical multi-objective optimization strategy to address this limitation. First, the numerical performance-trajectory mapping is derived based on a foot-ground contact model, aiming to decouple the performance characteristics. Subsequently, a hierarchical optimization strategy is employed for two types of CLM design scenarios: In trajectory shape-constrained scenarios, a coarse-to-fine optimization process, integrating Fourier descriptors, refines the design from overall shape to local features. In scenarios without trajectory shape constraints, a stepwise optimization process is proposed for reconfigurable CLMs to transition from primary motion to auxiliary motion. The robustness of the proposed design strategy is validated across three configurations and seven algorithms. The effectiveness of the proposed design strategy is verified by comparison with other existing CLM design methods. The applicability of the proposed strategy is confirmed through simulation and prototype experiments. The results demonstrate that the hierarchical strategy effectively addresses the challenges of precise performance design in CLMs. Our work provides a general framework for the CLM design and offers insights for the optimization design of other closed-chain linkages.