Adaptive Irregular Time-Varying Constraints Control for a Class of Underactuated Mechanical Systems

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State constraints are crucial for preventing system hazards by enforcing safety boundaries, yet ensuring state constraints for underactuated mechanical systems (UMSs) operating in complex environments remains unsolved due to their limited workspace and inherent underactuation. To address this critical safety issue involving unactuated states, this paper proposes a novel unified adaptive state-constraints control (UASCC) scheme based on sliding mode control (SMC) for a class of multi-input multi-output (MIMO) UMSs that do not satisfy the strict-feedback form. First, an innovative auxiliary term, integrating a nonlinear state-dependent function (NSDF) and the sliding mode variable signal, is designed to rigorously maintain all state variables within prescribed irregular time-varying constraints. Simultaneously, by designing a new time-dependent shifting function (TDSF), the proposed scheme allows for responses to irregular time-varying constraints under various scenarios without the need to modify the controller structure. Furthermore, this work eliminates the requirement for known uncertainty upper bounds in the SMC of UMSs. By introducing an adaptive time-varying control gain, the resulting continuous control scheme effectively mitigates controller gain overestimation and chattering, thereby enhancing the system’s transient performance. The system’s stability is rigorously proven through Lyapunov theory. Finally, the effectiveness of the proposed control method is experimentally validated on both a laboratory bridge crane platform and a four-degree-of-freedom (4-DOF) tower crane platform.

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