Holonomic bases, and drive shafts and roller assemblies that can be used in the holonomic bases. In some implementations, a holonomic base includes at least two pairs of roller assemblies, with each of the pairs being coupled to a corresponding drive shaft. In some of those implementations, each of the roller assemblies of each pair includes three roller segments that are each coupled to the corresponding drive shaft and that each include an exposed outward facing spherical zone that approximates a portion of the surface of a sphere. The roller segments of each roller assembly are in fixed relation to one another relative to the rotational axis of a drive shaft to which the roller assembly is coupled, but the roller segments each freely rotate about a corresponding roller segment rotational axis that extends outward from the drive shaft.