Satisfying Boundaries While Constraining Performance for Underactuated Mechanical Systems Control: A Novel Constraint-Following Approach

Addressing the control input limitations of underactuated mechanical systems presents a significant challenge in control engineering. In this paper, a novel constraint-following approach is proposed for the control design of underactuated systems with equality and inequality constraints. Notably, this control design relies solely on the system’s physical variables, obviating the need for auxiliary variables, such as Lagrange multipliers or pseudo variables. As a representative example, bicycle robots demonstrate the effectiveness of this constraint-following method by concurrently applying both types of constraints. Furthermore, this study employs a standard linear quadratic regulator (LQR) in simulations for comparative analysis, thereby underscoring the benefits of our proposed methodology. The innovative constraint-following approach not only offers solutions to the challenge of control input limitations in underactuated systems but also significantly enhances the utility of bicycle robots in human applications.