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Formations of multi-agent systems, such as mobile robots, satellites and aircraft, require individual agents to satisfy their kinematic equations while constantly maintaining interagent constraints. In this paper, we develop a systematic framework for studying formation motion feasibility of multi-agent systems. In particular, we consider formations wherein all the agents cooperate to enforce the formation. We determine algebraic conditions that guarantee formation feasibility given the individual agent kinematics. Our framework also enables us to obtain lower dimensional control systems describing the group kinematics while maintaining all formation constraints.