Estimation of human walking stability regions via zonotopic set‐membership

Abstract Falls in older adults present a critical public health challenge, underscoring the urgent need for reliable stability monitoring. Existing assessment methods, ranging from simplistic threshold‐based approaches to probabilistic estimators, often lack either robustness to model uncertainties or interpretable safety guarantees. This paper presents a novel framework for real‐time gait stability assessment by formulating it as a set‐membership state estimation problem under unknown‐but‐bounded (UBB) uncertainties. We introduce a time‐varying stability region, represented as a zonotope in the center of mass (COM) state space, which is empirically constructed from normal walking data. A zonotopic set‐membership filter (SMF) is then developed to propagate bounded uncertainties and recursively compute an enclosing set of the current state. Stability is certified via a sufficient set‐inclusion condition between the state set and the stability region; when this condition is violated, a convex distance‐to‐set metric provides a continuous risk score. Simulations and experimental studies demonstrate that the proposed estimator achieves interpretable, bounded‐error tracking of COM states. The results confirm its ability to discriminate between normal and disturbed gait with interpretable risk escalation, offering a principled foundation for wearable fall prevention systems.