Nonlinear analysis on purely mechanical stabilization of a wheeled inverted pendulum on a slope

Abstract: This paper investigates the potential for stabilizing an inverted pendulum without electric devices, using gravitational potential energy. We propose a wheeled mechanism on a slope, specifically, a wheeled double pendulum, whose second pendulum transforms gravity force into braking force that acts on the wheel. In this paper, we derive steady-state equations of this system and conduct nonlinear analysis to obtain parameter conditions under which the standing position of the first pendulum becomes asymptotically stable. In this asymptotically stable condition, the proposed mechanism descends the slope in a stable standing position, while dissipating gravitational potential energy via the brake mechanism. By numerically continuing the stability limits in the parameter space, we find that the stable parameter region is simply connected. This implies that the proposed mechanism can be robust against errors in parameter setting.