arXiv:2610.16223v1 Announce Type: new Abstract: Commercial balancing wheels are closed systems: an internal controller keeps the board upright, and a rider steers by shifting weight and twisting the hips. We augment a one-wheel with a lead-screw weight shift for longitudinal motion and a reaction wheel for yaw. The reaction wheel stores limited momentum, so a turn is a sequence of torque pulses, and whether a pulse rotates the body depends on static friction at the tire contact. From a 24-pulse torque sweep on one surface we fit a two-part model that gives the probability that a pulse rotates the body, treating the breakaway torque as random, and the rotation angle when it does; at maximum torque the posterior engagement probability is 0.54 (90% credible interval 0.24-0.84). The weight shift is modeled as a rate- limited input with a measured speed gain and an assumed first-order response, which predicts stopping distances four times those of a direct-force model. These models drive an event-triggered supervisor that schedules pulses by expected heading improvement, brakes when the predicted braking path would leave the safe set, tightens margins for model uncertainty, and updates the friction estimate online. In simulation on 500 plants drawn from the fitted models, the robust supervisor completed 92.6% of missions with 1.8% safety violations and 1.6% safe aborts, versus 84.0% and 7.2% for a supervisor using mean models and 1.8% and 20.4% for a baseline that ignores friction. A video of the hardware experiments is available online (https://github.com/ASAS-Labs/x-wheel).