Pareto optimal synthesis of eight-bar mechanism using meta-heuristic multi-objective search approaches: application to bipedal gait generation

The structural complexity of the bipedal locomotion may be reduced by using mechanisms with fewer actuators, which ideally do not degrade the performance and functionality of the robot. However, when the mechanism design considers conflicting design objectives, the search for design solutions with specific trade-offs becomes hard. This work studies different multi-objective search approaches the dominance-based, the decomposition-based and the metric-driven in the dimensional synthesis of the eight-bar mechanism for the bipedal locomotion application in the sagittal plane stated as a mixed discrete-continuous nonlinear multi-objective optimisation problem. This work also proposes a dominance-based multi-objective differential evolution algorithm called Multi-Objective Specialist Population-based Differential Evolution (MOSPDE), which endows specialised subpopulations to exploit different regions of the Pareto front to favour the search for design trade-offs with a suitable generation of the gait and force transmission during the stance phase. The comparative study includes algorithms reported in the specialised literature based on dominance (MOPSO, MODE variants and NSGA-II), decomposition (MOEA/D-DE) and metric-driven (SMS-EMOA). The statistical analysis reveals that using the Pareto dominance search approach based on differential evolution and the inclusion of exhaustive exploitation can promote the reconfigurability of the bipedal locomotion mechanism with better trade-offs that satisfy the conflicting design objectives.