Robust Gain Scheduling Control Design for Robotic Position Control: Cane Platform Implementation

This paper presents a robust H ∞ control framework for nonlinear robotic systems using Takagi-Sugeno modeling with PCA-based model reduction. The approach transforms second-order matrix dynamics into polytopic Linear Parameter Varying representations, reducing computational complexity from exponential vertex growth through principal component analysis while preserving a prescribed percentage of system energy. Sufficient LMI conditions guarantee closed-loop stability and prescribed disturbance attenuation with explicit stability region characterization. The methodology is validated on an omnidirectional mobile platform supporting an inverted pendulum cane for elderly assistance, demonstrating superior disturbance rejection and smooth control transitions. Simulation results confirm theoretical guarantees with exponential convergence and constraint satisfaction.