Determining the domain of stable human sit-to-stand motions via controlled invariant sets and backward reachability

Falls during sit-to-stand are a common cause of injury. The ability to perform this movement with ease is itself correlated with a lower likelihood of falling. However, a rigorous mathematical understanding of stability during sit-to-stand does not currently exist, particularly in different environments and under different movement control strategies. Having the means to isolate the different factors contributing to instability during sit-to-stand could have great clinical utility, guiding the treatment of fall-prone individuals. In this work, we show that the region of stable human movement during sit-to-stand can be formulated as the backward reachable set of a controlled invariant target, even under state-dependent input constraints representing variability in the environment. This region represents the ‘best-case’ boundaries of stable sit-to-stand motion. We call this the stabilizable region and show that it can be easily computed using existing backward reachability tools. Using a dataset of humans performing sitto-stand under perturbations, we also demonstrate that the controlled invariance and backward reachability approach is better able to differentiate between a true loss of stability versus a change in control strategy, as compared with other methods.