Adaptive Optimal Motion Control of Uncertain Underactuated Mechatronic Systems With Actuator Constraints

Underactuated mechatronic systems are widely used in industrial production, where the control efforts and operation accuracy are both important aspects of performance evaluations. Hence, how to realize effective motion control, while reducing control efforts as much as possible, becomes an open problem for underactuated systems. Although some open loop approaches (e.g., trajectory planning) take energy optimization into account, they need linearization/approximation manipulations and exhibit weak robustness, which is prone to degrading practical control performance. To this end, this article proposes an adaptive tracking controller for uncertain multi-input-multi- output (MIMO) underactuated mechatronic systems, to fulfill accurate positioning/tracking control with saturated inputs and reduce control efforts as well. Particularly, by elaborately developing an auxiliary compensation term and a robust term, the proposed controller ensures asymptotic convergence of both actuated and unactuated variables. Meanwhile, the modified performance index function is approximated online and introduced into the Lyapunov function candidate to make the stability analysis process more concise. To the best of our knowledge, without the need of offline computation and the persistence of excitation (PE) condition, this article presents the first adaptive optimal controller to simultaneously achieve error elimination, control effort optimization, and actuator constraints for a class of underactuated systems. Finally, strict theoretical analysis and experimental validations show the effectiveness and robustness of the suggested controller.

I. Introduction

Due to simpler structures, higher flexibility, lower energy consumption, etc., underactuated mechatronic systems play increasingly important roles in the fields of industry, aerospace, manufacturing, etc., such as wheeled inverted pendulums [1], cranes [2]–[4], unmanned aerial vehicles [5], underactuated robots [6]–[7], etc. These kinds of systems not only exhibit high uncertainties [8]–[9] and nonlinearity [10]–[12], but also have fewer actuators than to-be-controlled degrees of freedom (DOFs), which brings additional challenges to controller design and analysis. Moreover, complicated nonholonomic constraints or coupling relationships between actuated and unactuated variables also increase the control difficulty. More importantly, different from full-actuated systems, it is quite difficult to ensure the transient performance of unactuated variables due to the lack of control signals. Currently, the control problems of underactuated systems have drawn much attention [13]–[17], including adaptive control [18], energy-based control [19], sliding mode control [20]–[21], model predictive control [22], etc.