  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.
