Back-support exoskeletons (BSEs) offer significant potential for reducing lumbar load and preventing lower-back injuries; however, their control is complicated by strong inter-channel coupling, time delays in actuation and sensing, and uncertainties induced by human–robot interaction. This paper develops a unified dynamic–kinematic model for a multi-input multi-output BSE that explicitly accounts for coupling effects, compliance, and delay characteristics, providing a control-oriented and physically consistent foundation. Based on this model, a prescribed performance control (PPC) framework is proposed to guarantee bounded tracking errors with predefined transient and steady-state behaviour in the presence of multidimensional, time-varying delays, without requiring model decoupling. To enhance robustness against lumped uncertainties, a hybrid observer integrating a linear extended state observer and a sliding mode observer is designed for real-time disturbance estimation and compensation. Simulation results obtained on a biomechanically realistic BSE platform demonstrate that the proposed PPC–LESO–SMO scheme achieves superior tracking accuracy, robustness, and convergence speed compared with conventional PPC and existing observer-based control approaches.
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