Abstract
Due to limited workspace and safety requirements for practical underactuated mechanical systems, it is necessary to restrict all to-be-controlled variables and their velocities within preset ranges, avoid collisions/overshoots, and improve braking performance. However, due to fewer available control inputs, it is quite challenging to ensure error elimination and full-state constraints for both actuated/unactuated variables, including displacements/angles and their derivatives (i.e., velocity signals) together. To handle the above issues, this article designs a new adaptive full-state constraint controller for a class of uncertain multi-input-multi-output (MIMO) underactuated systems. First, different output constraint-related auxiliary functions are constructed in the Lyapunov function candidate to generate nonlinear displacement-/angle-limited terms to control all state variables. Then, this article handles velocity constraints in a new manner, where the elaborately designed velocity constraint-related terms are directly introduced into the presented controller (instead of the Lyapunov function candidate), and strict theoretical analysis is provided by utilizing reduction to absurdity. Hence, both actuated and unactuated velocity constraints are ensured to further improve transient performance. In addition, the impact of model uncertainties is addressed online to realize accurate positioning control for all state variables. Compared with current studies of underactuated systems, this article presents the first adaptive controller to address output and velocity constraints for actuated and unactuated variables together; moreover, their asymptotic convergence is proven by strict stability analysis, which is important both theoretically and practically. In the end, the feasibility and robustness of the proposed controller are verified by hardware experiments.
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