This paper presents a four-pendulum design for an omnidirectional spherical robot. The robot moves by the rotation of tetrahedrally-located pendulums to change the center of mass, and can do so instantaneously in any direction. In that respect, it is omnidirectional unlike the more common single-pendulum designs. In the paper, the theoretical design is discussed and contrasted to existing theoretical center-of-mass designs in terms of directionality, torque arm, eccentricity, and radius of gyration. The torque arm comparison is based on the envelope of the dynamically-controlled mass (i.e., how far in any direction can the center of mass be moved), while the eccentricity and gyration criteria are based on homogeneity and size of the mass moment of inertia (i.e., how much does the design "wobble" while rolling; how much inertia does it have). In these regards, the four-pendulum architecture is better than some in one respect, better than many in other respects. A prototype has been built and tested to successfully implement the four-pendulum propulsion. Significance of the proposed system is presented through a comparison of results with previous work.
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