In this paper, presented is an approach for the control of swarm motions that treats a swarm as a deformable body or a continuum. By considering a special class of motion maps between a current configuration prescribed at a given time t and a desired configuration prescribed at a subsequent time t+Δt called a homogeneous map two strategies are proposed for the control of a swarm or a multi-agent system (MAS). In the first strategy, MAS motion control is achieved with no communication among agents in the idealized case where the required map from any t to t+Δt may be predetermined. It is the case when a desired swarm task can be scripted ahead of time with some certainty. The second control strategy is based on three leaders prescribing the motion map for a desired swarm task which is then propagated to the followers via a local inter-agent communication protocol. The proposed communication protocol exploits some special features of homogeneous maps. It achieves the desired MAS motion control with three leaders and minimum inter-agent communications. Simulation results validate the effectiveness of the proposed strategies.