指数座標を用いた倒立二輪ロボットのモデル化とその移動制御への応用

抄録

A control design method using the partial linearization and zero dynamics has been proposed for high-speed movement of inverted two-wheeled robots. Moving distance can be specified by solving the zero dynamics with respect to the control variables. However, except for simple systems such as symmetric one-body-link systems, deriving the zero dynamics is generally intractable. In this research, we propose the system modelling and control of the robots using the exponential coordinates. In the coordinates, the system dynamics are obtained in closed form, so we can design various types of controllers by using them. Moreover, the system parameters representing the system structures (geometrical/topological) are appeared explicitly in the dynamics, and they can be easily changed. Hence the formula of the dynamics will be also useful for system designs. As a first step for the optimal system design of the robots, we consider modeling and control of the inverted two-wheeled robots in the exponential coordinates. Owing to the closed form formula of the dynamics, the control design method using the zero dynamics can be employed. The desired variables for the PD controller are obtained by solving an optimization problem involving the zero dynamics. Numerical examples are conducted to illustrate the proposed method.