Balance Map Analysis as a Measure of Walking Balance Based on Pendulum-Like Leg Movements

Abstract

This paper proposes an analysis of walking balance in terms of movements of stance and swing legs based on an inverted pendulum and a simple pendulum. Linearization, decoupling, and non-dimensionalization of a compass gait model enable to characterize the relationship of the trajectories between the stance and swing legs by only two parameters (energy ratio and phase difference). The energy ratio is defined by the ratio of the orbital energy between the pendulums. The phase difference represents the position of the stance leg in relation to the swing leg. This study considers an orbital energy conservation of a step transition and analyzes reachability of a desirable touchdown condition. If the time evolution from a current state is not reachable to the desired touchdown region, the state is labeled as a state in balance loss. By analyzing the reachability limits of the energy ratio and phase difference, we illustrate the balance loss and safe regions on the state space of the inverted pendulum, which is termed as balance map. We examined the effects of the simplification and linearization of the compass gait model by using computer simulations. Through the simulations of walking with perturbations, we confirmed that the balance map analysis could predict a future fall in an early phase for even trajectories derived by the nonlinear model.