A determinant of the leg swing trajectory during walking

When we walk, there are infinite number of possible trajectories for leg swing. How does the brain design the trajectory? As a candidate for the strategy of the trajectory selection, we assessed the criterion of the minimization of the energy cost in this study. We computed the optimal leg trajectory that minimizes the energy cost during the swing phase under the boundary condition that enables the smooth taking off and the grounding. The obtained trajectory exhibits the following characteristics. (1) In the beginning of swing the foot is thrown backward and raised up because of large forward torque at the hip joint and small torque at the knee joint. (2) The maximum height of the foot becomes larger as walking speed becomes faster. (3) In the latter half of swing the foot is thrown forward and the speed takes its maximum value, and then (4) the foot is retracted by large torques at a hip and knee joint just before the grounding. These characteristics are well coincident with those observed in human leg swing, which would indicate that the leg swing trajectory be planned so as to minimize the energy cost.