  People with lower-limb loss, the majority of which use passive prostheses,
exhibit a high incidence of falls each year. Powered lower-limb prostheses have
the potential to reduce fall rates by actively helping the user recover from a
stumble, but the unpredictability of the human response makes it difficult to
design controllers that ensure a successful recovery. This paper presents a
method called TRIP-RTD (Trip Recovery in Prostheses via Reachability-based
Trajectory Design) for online trajectory planning in a knee prosthesis during
and after a stumble that can accommodate a set of possible predictions of human
behavior. Using this predicted set of human behavior, the proposed method
computes a parameterized reachable set of trajectories for the human-prosthesis
system. To ensure safety at run-time, TRIP-RTD selects a trajectory for the
prosthesis that guarantees that all possible states of the human-prosthesis
system at touchdown arrive in the basin of attraction of the nominal behavior
of the system. In simulated stumble experiments where a nominal phase-based
controller was unable to help the system recover, TRIP-RTD produced
trajectories in under 101 ms that led to successful recoveries for all feasible
solutions found.
