Dynamic performance evaluation of evolutionary multi-objective optimization algorithms for gait cycle optimization of a 25-DOFs NAO humanoid robot

Abstract

Researchers are increasingly using optimization methods to achieve optimal dynamic performance of humanoid robots, often involving multiple conflicting objectives. Multi-objective optimization algorithms (MOAs) aim to find a Pareto front of optimal solutions, but selecting the best algorithm based on solution quality and computational efficiency remains challenging. This study comprehensively evaluates MOAs from different paradigms: swarm intelligence (CMOPSO), genetic algorithms (NSGA-II, DCNSGA-III), and decomposition-based approaches (CMOEA/D) for optimizing the gait cycle of a 25 DOF NAO humanoid robot during single support phase (SSP) and double support phase (DSP) scenarios. The algorithms’ convergence, diversity, and constraint-handling capabilities are systematically analyzed in solving the gait generation problem. The bi-objective optimization simultaneously minimizes power consumption and maximizes dynamic stability subject to eight functional constraints with 12-13 decision parameters. Through performance evaluation using running inverted generational distance (IGD) and hypervolume (HV) metrics across eleven independent runs of each algorithm, NSGA-II emerges as the most suitable algorithm, demonstrating superior convergence and solution quality, while CMOPSO shows competitive performance with faster initial convergence. DCNSGA-III exhibits moderate performance with constraint-handling difficulties, and CMOEA/D demonstrates poor convergence characteristics requiring significantly more computational resources. Two distinct knee regions emerge during both SSP and DSP, representing optimal trade-off solutions, with a systematic framework provided for practitioners to select appropriate gait parameters based on operational priorities. The running IGD metric combined with HV validation demonstrates effectiveness in providing robust algorithmic insights, enabling practitioners to select suitable algorithms for similar complex real-world optimization problems.