Cluster space control is a method of multirobot formation keeping that considers a group of robots to be a single entity, defining state variables to represent characteristics of the group, such as position, orientation, and shape. This technique, however, suffers from singularities when a minimal state representation is used. This paper presents three alternative implementations of this control approach that eliminate singularities through changes in the control architecture or through redundant formation definitions. These proposed solutions rely on quaternions, dual quaternions, and control implementations that produce singularity-free trajectories while maintaining a cluster level abstraction that allows for simple This work has been sponsored through USAIT Grant W911NF-14-1-0008, ITBACyT 2013-17, and Agencia Nacional de Promoción Científica y Tecnológica, FONCYT PICT 2014-2055.