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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 sit-to-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. 

This paper presents a new model and phase-variable controller for sit-to-stand motion in above-knee amputees. The model captures the effect of work done by the sound side and residual limb on the prosthesis, while modeling only the prosthetic knee and ankle with a healthy hip joint that connects the thigh to the torso. The controller is parametrized by a biomechanical phase variable rather than time and is analyzed in simulation using the model. We show that this controller performs well with minimal tuning, under a range of realistic initial conditions and biological parameters such as height and body mass. The controller generates kinematic trajectories that are comparable to experimentally observed trajectories in non-amputees. Furthermore, the torques commanded by the controller are consistent with torque profiles and peak values of normative human sit-to-stand motion. Rise times measured in simulation and in non-amputee experiments are also similar. Finally, we compare the presented controller with a baseline proportional-derivative controller demonstrating the advantages of the phase-based design over a set-point based design.