Decoupled MPC for ZMP-Based Lateral Stability in Two-Wheeled Inverted Pendulum with Roll Joint

This paper presents a linear model predictive control (MPC) framework for a two-wheeled inverted pendulum with a roll joint (TWIP-R). Traditional linear quadratic regulator (LQR) approaches effectively stabilize the sagittal motion of two-wheeled inverted pendulums (TWIP), but fail to account for lateral dynamics and constraint handling during curved trajectories. Our approach decouples the system into pitch, yaw, and roll subsystems, each controlled by a dedicated linear MPC. By predicting lateral inertial forces from the reference velocity and yaw rate, the roll controller computes the zero moment point (ZMP) deviation and incorporates it into both the cost and constraints for proactive stabilization. Simulation results on a figure-eight trajectory demonstrate precise velocity tracking, robust lateral balance, and feasibility, highlighting the potential of the proposed method for dynamic, constraint-aware robot control.