Persistent homology for automatic determination of human-data based cost of bipedal walking

Robotic walking research, since its inception, has attempted to generate anthropomorphic gait, but the community as a whole has struggled to agree even upon the correct ordering of discrete events during walking. In this paper, we propose a universal temporal ordering of discrete events for bipedal walking based on motion capture data collected from a nine subject straight line walking experiment. To construct this ordering, we develop a technique based on persistent homology to process the motion capture data to determine when the number of contact points changes during the course of a step which automatically dictates the ordering of discrete events. Surprisingly the findings of this work are that every subject regardless of age, sex, weight or height in the experiment had an identical temporal ordering of such events. This result allows for the development of a universal anthropomorphic bipedal robotic walking model because the temporal ordering of events together with the Lagrangian modeling of the robot completely determines the mathematical model of the system. Importantly, this universal ordering allows us to propose a cost function based on human data: the human-based cost, which we use to gauge the “human-like” quality of robotic walking.