Frontal-Sagittal Dynamic Coupling in the Optimal Design of a Passive Bipedal Walker

The parametric design of passive bipedal walkers (PBWs) has been addressed by considering its dynamics in sagittal plane only. Nevertheless, with the aim of obtaining a complete parametric description, frontal plane dynamics must also be involved. Hence, in order to obtain a synergetic design of a PBW that simultaneously couples operating requirements of both planes, a concurrent design problem is proposed. The concurrent design approach is established as a nonlinear discontinuous dynamic optimization problem with mixed design variables and is solved by using four variants of differential evolution (DE) algorithm. The reduction in differences among Poincaré mapping values related to consecutive gait cycles is proposed as the performance function, where its minimization must induce the convergence toward a limit cycle in PBW frontal and sagittal planes. A comparative analysis between the proposed concurrent design and a sequential design process is carried out for a particular case study: the PBW with single joint and curved feet. The simulation results show the advantages of the obtained concurrent design solutions to provide stable gait cycles in both PBW planes. In addition, the statistical analysis of the applied DE variants indicates that DE/best/1/bin promotes an efficient tradeoff between exploration and exploitation of solutions in the objective space. For the particular problem, this results in a high design reconfigurability, mainly associated with the material assignment diversity provided by the optimizer.