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A dynamics-based posture-balancing control strategy for a new one-wheel pendulum robot (OWPR) is proposed and verified. The OWPR model includes a rolling wheel, a robot body with a steering axis, and a pendulum for lateral balancing. In constructing the dynamic model, three elements are generalized in comparison with existing robotic systems: the mass and inertia of the robot body, the “I”-type pendulum, and the steering motion. The dynamics of the robot are derived using a Lagrangian formulation to represent the torques of the wheel during the rolling, yawing, and pitching of the robot body, in terms of the control inputs. The OWPR dynamics are decomposed into state-space models for lateral balancing and steering, and the corresponding controller is designed to be adaptive to changes in the state variables. Simulations and experimental studies are presented that demonstrate and verify the efficiency of the proposed models and the control algorithm.