Several concepts and results in geometric mechanics are used to analyze and control the locomotion system of an unconventional robot encapsulated in a sphere shell, assumed to roll without slipping on the floor and internally equipped with a set of inertia gyros as indirect driving devices. Lie group symmetries intrinsic to this problem, i.e. invariance of the system’s Lagrangian and velocity distribution to some group of motions, allows the reduction of the equations of motion. This system whose motion ability is based on angular momentum conservation is established as a controllable nonholonomic system for which the attitude/position cannot be stabilized by smooth feedback laws. Pursuing the reduction process permits to design a feedback law extensible to both kinematic and dynamic levels of actuation, enabling the robot to execute finite-time reorientation and repositioning maneuvers while confined to move in corridor-like domains. As an extra application, this system is also intended to provide an attitude control testbed that, in certain senses, emulates the dynamics of on-orbit conditions, allowing a near-to-reality evaluation of path planning and feedback control algorithms for satellites. A concurrent solution to the attitude tracking control problem is proposed that, due to parameters uncertainties, is likely to require effective adaptive aptitudes. Key Words: Geometric Mechanics, Dynamics Analogy, Adaptive Attitude Control, Nonholonomic Control, Reduction by Symmetry, Autonomous Locomotion .
