Every year, 2.5 million people visit the emergency department accounting for $34 billion in hospital visits, stays and treatment. Financial considerations aside, falling once results in the fear of falling further increasing the likelihood of falling. For the past few decades, much work has gone into identifying those likely of falling or those who are stable by determining features that distinguish fallers from non-fallers. The holy grail of such an identification scheme would inform how much perturbation the subject can reject, which is also known as the basin of stability. The more perturbation that can be rejected, the larger the basin of stability is and the more stable the individual is. However, determining this basin of stability experimentally is an impractical task. Rather than performing perturbation experiments, recent advances in control theory and reachability analysis allow us to compute this basin of stability in simulation.

In this thesis, we present a personalized and automated framework for computing the basin of stability for human motion. To do this, we first develop a tool to compute the basin of stability for dynamical systems and apply this to human motion. The utility of this framework is illustrated on the Sit-to-Stand task, though it can handle more general motions such as gait. The framework is broken down into three components. First, a representative hybrid model is chosen for the standing motion. Second, a controller is constructed to track the motion using optimal control and PD control. Third, using recent advances in hybrid occupation measures, an outer-approximation of the basin of stability is computed. We study the Sit-to-Stand action of 15 subjects (10 young and 5 older) and the computed basin of stability can differentiate between less and more stable Sit-to-Stand strategies. The contributions are the first steps towards developing a numerical method for determining the basin of stability of human motion.




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