Smoothly Weighted Hybrid NMPC–LQR Control for Slope-Dependent Uphill Motion of a Two-Wheeled Self-Balancing Wheelchair

Sustained uphill motion of two-wheeled self-balancing wheelchairs is challenging. Slope-induced gravity changes the equilibrium condition, driving-torque demand, and velocity response. This paper proposes a smoothly weighted hybrid control method. The method combines nonlinear model predictive control and a linear quadratic regulator for pitch stabilization and uphill velocity tracking. The control design accounts for the slope-dependent equilibrium condition and steady-state torque demand. NMPC handles large-deviation recovery, velocity regulation, and actuator constraints. LQR improves local stabilization near the equilibrium point. The two controller outputs are coordinated by a continuously varying weight, which provides a smooth transfer of control authority across the transition region. MATLAB/Simulink simulations compare the proposed method with standalone NMPC, LQR, and SMC under several slope angles. Disturbance-recovery tests are also conducted under external torque disturbances. The results show stable uphill motion under the tested slope conditions. After finite-duration disturbances, the controller recovers both pitch posture and uphill velocity. Under a sustained torque disturbance, pitch stability is retained, but velocity regulation degrades. The proposed method improves pitch stabilization and velocity maintenance under the tested conditions. The recorded wheel-end torque remains bounded without sustained saturation in the three hybrid-controller cases. These results demonstrate numerical feasibility under the specified nominal simulation conditions, while uncertainty-robust and real-time performance remain to be validated.