Nonlinear Incremental Optimal Control for Underactuated Mechanical Systems

Abstract

Underactuated mechanical systems (UMS) feature prominently in robotics and aerospace, with aircraft, unmanned air vehicles, and aeroelastic wings as prime examples. These systems present multifaceted control challenges, ranging from inherent underactuation and stability concerns to state and control saturation and an overarching need for robustness. Crucially, reducing model dependency is a key strategy to enhance control robustness. Nonlinear Model Predictive Control (NMPC) is valued for addressing underactuation and constraints within complex nonlinear dynamics while considering future stages for immediate decision-making. However, implementing NMPC in UMS can pose challenges due to model uncertainties and external disturbances. To enhance NMPC's robustness in UMS control, we introduce a disturbance rejection NMPC strategy, which is tightly coupled with the incremental nonlinear dynamic inversion (INDI), a sensor-based adaptive control approach. The INDI is expected to reject most of the disturbances. Any disturbance residues are managed within a robust NMPC framework through constraint tightening. The efficacy of our method is exemplified through its application to two distinct UMS models. The proposed controller is first customized for a nonlinear aeroelastic system. Compared to the nominal NMPC, the simulation studies demonstrate up to 37.60% and 40.00% error reductions in plunge and pitch motions. Subsequently, we adapt this controller for quadrotor trajectory tracking tasks and compare the results with a benchmark control strategy that loosely coupled the NMPC with INDI. Extensive simulation validations have been performed to track agile trajectories, showing up to a 79.58% reduction in position error and up to a
44.08% reduction in heading error.