Approach to Gait Coordination: Adaptive Fuzzy Finite-Time Control of a Stochastic Prosthesis-Human Symbiosis With Intentional Delay

Abstract

The generation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">intentional delay</i> in response to the stride frequency is seldom considered in prosthesis-human symbiosis (PHS). Unfortunately, such intentionally delayed human-robot interaction poses a new challenge to their gait coordination (GC) in stochastic environments. Utilizing fuzzy logic systems (FLSs), we investigate an adaptive fuzzy finite-time control of a stochastic PHS with intentional delay to address this issue. Noting that the intentional delay is related to walking velocity, this article conducts experiments on ten healthy subjects to identify the intentional delays at different velocities using the FLS. Introducing the FLS-identified delay and contralateral healthy limb gaits, we propose a prosthetic gait planner to simultaneously determine the reference stride frequency and stride length, thus properly regulating the desired velocity. Considering the adverse effects of the required intentional delay and state constraints in the stochastic framework, we propose a new statistical Lyapunov–Krasovskii functional, together with a Tan-type barrier Lyapunov function. Correspondingly, an adaptive fuzzy controller is developed via a backstepping design, thus solving the semi-global finite-time stable in probability with intentional delay, unknown nonlinearities, and state constraints. Application studies validate the efficacy of the proposed approach. The results show that our approach can predict walking behavior while performing GC.