Multi-stage trajectory tracking control design under comprehensive constraints based on Generalized Udwadia–Kalaba theory

Abstract

A novel control design based on Generalized Udwadia–Kalaba (GUK) theory is proposed to achieve the trajectory tracking under comprehensive constraints in this paper. To describe the complex task requirements, a constraint framework including equality and inequality constraints is constructed. Thus, the complex trajectory tracking problem is converted into a constraint-following problem. Based on the framework above, GUK equation is introduced to consider the equality and inequality constraints individually. Specifically, the equality constraints are transformed into second-order matrix form, while the inequality constraints are addressed via a diffeomorphism. Then, a novel control method including servo control term and high-order control term is proposed. Through these two control terms, the constraint forces for equality and inequality can be solved separately. The effectiveness of this control method is verified by the stability analysis based on Lyapunov minimax apprach and illustrative application of unmanned surface vehicle (USV). Meanwhile, the superiority of this method is demonstrated through a comparative analysis with Udwadia–Kalaba (UK) method, Linear Quadratic Regulator (LQR) method and sliding mode control (SMC) method.