Convex Computation of the Basin of Stability to Measure the Likelihood of Falling: A Case Study on the Sit-to-Stand Task

Abstract: Locomotion in the real world involves unexpected perturbations, and therefore requires strategies to maintain stability to successfully execute desired behaviours. Ensuring the safety of locomoting systems therefore necessitates a quantitative metric for stability. Due to the difficulty of determining the set of perturbations that induce failure, researchers have used a variety of features as a proxy to describe stability. This paper utilises recent advances in dynamical systems theory to develop a personalised, automated framework to compute the set of perturbations from which a system can avoid failure, which is known as the basin of stability. The approach tracks human motion to synthesise a control input that is analysed to measure the basin of stability. The utility of this analysis is verified on a Sit-to-Stand task performed by 15 individuals. The experiment illustrates that the computed basin of stability for each individual can successfully differentiate between less and more stable Sit-to-Stand strategies.