Integrating Gain-Scheduling and Polynomial Interpolation with the Linear-Quadratic Regulation Approach for Enhancing the Nonlinear Performance of a Robotic Arm

In the realm of nonlinear control, where complex dynamics and trajectory variations pose substantial challenges, this work presents an enhancement to the traditional Linear-Quadratic Regulator (LQR) approach by incorporating polynomial interpolation of the gains. This approach synergizes the robustness of LQR for regulation and stabilization with the adaptability of polynomial gain scheduling, enabling continuous and responsive control across a wide range of trajectories. The integration not only enhances system accuracy but also significantly improves stability under nonlinear conditions. Dynamical simulations performed in Matlab/Simulink with the Simscape Multibody toolbox reveal that the proposed polynomial gain scheduling method considerably reduces control error compared to the classical LQR, particularly in the presence of nonlinear disturbances such as dry friction.