This paper investigates a group of multiagents moving on a 2-D plane with a constant speed but maneuverable headings. It is called a minimal control multiagent model (MCMA) when each agent employs a static decentralized control law that relies on its neighbors' relative positions with respect to its local reference frame. In other words, the control law does not involve any complicated velocity measurement or estimation mechanism. Various minimal multiagent models have been investigated and extensively simulated in terms of their collaborative behaviors. This paper, for the first time, gives rigorous theoretical proofs for the functionalities of an MCMA model in both collision avoidance and velocity alignment.