Robust Constraint-Following Control for Uncertain Mechanical Systems With Generalized Udwadia-Kalaba Approach
Zicheng Zhu, Jun Ma, Wenxin Wang, Yuanjie Xian, Hao Sun, Han Zhao, Tong Heng Lee
Abstract
In this letter, we propose a robust constraint-following control approach for uncertain mechanical systems under both equality and inequality constraints. Particularly, both the global and local inequality constraints are systematically incorporated into the Udwadia-Kalaba (U-K) equation leveraging the diffeomorphism technique, wherein a novel smooth approximation of the local inequality constraints is proposed to address the non-differentiability resulting from its spatiotemporal dependence nature. Based on this development, the generalized U-K equation is mathematically established. With this, we develop a robust constraint-following control strategy to ensure satisfying system performance in the presence of uncertainties and various constraints. Moreover, by Lyapunov minimax approach, the proposed control strategy guarantees both uniform boundedness (UB) and uniform ultimate boundedness (UUB) of the system. Finally, numerical simulations on the lateral motion control of an autonomous vehicle demonstrate the effectiveness of the proposed approach.