Optimal wheel size selection in mobile robots is pivotal in addressing the challenges posed by varying surfaces, navigating complex environments, ensuring stability, and optimizing energy consumption. Targeting this key feature, this article introduces the improbability roller, a mobile robot with two variable-diameter wheels designed to illustrate the significance of wheel size in achieving adaptability and enhancing overall traversability capabilities. The uniqueness of the robot lies in its dynamic ability to adjust the wheel diameter, a mechanism that empowers it to seamlessly switch between different terrains and tasks, by utilizing only three actuators to drive forward/backward, steer, and change the wheel diameters independently. This study not only presents the design of the robot, but also delves into the development of a kinematic model, an open-loop control strategy, and an extensive series of experiments aimed at validating its performance. Through experiments on trajectory tracking, diameter adjustment speeds, steering angle effects, slope climbing capabilities, and energy efficiency considerations, this article underscores the crucial role that a variable-diameter wheel plays in shaping the operational envelope of mobile robots.
