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.

Nonlinear Optimal Control for the Wheeled Inverted Pendulum System

“…This control problem is of interest for the area of robotics because such a type of two-wheeled vehicles can be used for the transportation of humans and loads without the space and maneuvering limitations exhibited by four-wheel vehicles. [3][4][5][6] Previous attempts to solve this problem have been based primarily on global linearization control method and state-space transformation approaches. [7][8][9][10] However, one can find also several results based on approximate linearization techniques.…”

Attitude control of inverted pendulums using reaction wheels: Comparison between using one and two actuators

“…Several studies have investigated the RWP. 17–27 RWP was first introduced by Spong et al, 17 where feedback linearization and passivity-based control were used for swing up and control. Hernández 18 proposed a control strategy that combined sliding modes and generalized PI control for swinging up and controlling the RWP around its unstable equilibrium point.…”