Gain-Scheduled Control of a Wheeled Inverted-Pendulum Robot with Load-Induced Equilibrium Drift Compensation

Wheeled inverted-pendulum robots with movable upper structures and variable payloads exhibit configuration-dependent equilibrium drift and payload-dependent dynamic variation, which complicate balancing control. This paper proposes a gain-scheduled controller–observer framework for payload-adaptive balancing of such a robot. First, the multi-body system is reduced to a control-oriented equivalent inverted-pendulum model through center-of-mass lumping, from which a parameter-varying linearized model is established. On this basis, an H∞ state-feedback controller with input constraints is synthesized in a linear matrix inequality (LMI) framework, and an augmented-state observer is designed to estimate the residual equilibrium offset induced by payload variation. To improve robustness over the operating range, the frozen-point design is extended to a sampled-model multi-model synthesis framework, and gain scheduling is implemented with respect to the measurable arm angle. Nonlinear Simscape simulations show that the proposed method can recover balance at representative fixed operating points, compensate effectively for load-induced equilibrium drifts, and preserve stable balancing performance under slow arm-angle variation. Quantitative comparisons with an LQR baseline further support the effectiveness of the proposed framework for payload-adaptive balancing control.