Dynamic model and boundary control for mechanical systems with inequality constraints: A generalized Udwadia–Kalaba approach

In this paper, a novel method for integrating equality constraints and inequality constraints is proposed for dynamic modeling of mechanical systems. The equality constraints are used to delineate the ideal trajectory of the actuator, while inequality constraints are applied to artificially set the error boundaries of the system states with uncertainty. Then, a robust control including two portions is designed based on the generalized Udwadia–Kalaba equation. The first portion implements constraint-following control by ensuring that the nominal system adheres to the desired trajectory according to the control force based on the equality constraints. The second portion utilizes the state transformation method, which enables the fluctuations of the system state error to be strictly limited to the inequality constraints. Based on the Lyapunov approach, the uncertainties can be compensated when both equality and inequality constraints are present. The uniform boundedness and uniform ultimate boundedness of the mechanical system can be guaranteed. At last, the feasibility of the model and control method based on the generalized Udwadia–Kalaba equation is proved by applying a robotic arm system. The verification are performed compared with other methods.