Optimizing toe joint stiffness to improve human-like walking.

The human metatarsophalangeal joint-often referred to as the "toe joint"-plays a vital role in gait by supporting body weight during mid-stance, enabling smooth rollover from heel to toe, and facilitating effective push-off in terminal stance. However, identifying its optimal stiffness remains challenging despite its relevance to both biological and robotic locomotion. In this study, we used a simulation-based trajectory optimization approach to investigate toe joint stiffness in a bipedal model. The results revealed that lower stiffness facilitated rollover while higher stiffness enhanced push-off. Because continuously varying stiffness is impractical in most passive devices, we extracted a single representative value (0.98 Nm/deg) by averaging the time-varying stiffness during the push-off phase. We then conducted a human walking experiment using adjustable toe joint boots across multiple stiffness conditions. The 0.98 Nm/deg condition yielded the highest subjective satisfaction and favorable spatiotemporal outcomes, especially among participants with anthropometry similar to the simulation model. Although direct numerical comparison between simulation and experiment was not performed due to modeling simplifications, key qualitative trends-such as toe joint moment progression and heel-off timing-were consistent. These findings highlight the potential of toe joint stiffness tuning to improve walking performance and user experience.