This paper addresses the problem of a spherical robot having an axisymmetric pendulum drive and rolling without slipping on a vibrating plane. It is shown that this system admits partial solutions (steady rotations) for which the pendulum rotates about its vertical symmetry axis. Special attention is given to problems of stability and stabilization of these solutions. An analysis of the constraint reaction is performed, and parameter regions are identified in which a stabilization of the spherical robot is possible without it losing contact with the plane. It is shown that the partial solutions can be stabilized by varying the angular velocity of rotation of the pendulum about its symmetry axis, and that the rotation of the pendulum is a necessary condition for stabilization without the robot losing contact with the plane.

本文解决了一个球面机器人的问题，该机器人具有轴对称的摆锤驱动并且在振动平面上滑动而不滚动。结果表明，该系统允许偏摆绕其垂直对称轴旋转的部分解（稳定旋转）。特别注意这些解决方案的稳定性和稳定性问题。进行约束反应的分析，并确定参数区域，其中球形机器人可以稳定而不失去与平面的接触。结果表明，可以通过改变摆绕其对称轴的旋转角速度来稳定部分解，并且摆的旋转是稳定的必要条件，而机器人不会失去与平面的接触。