In this paper, a multi agent system (MAS) is considered as particles of a continuum deforming under a specific class of homeomorphic mappings, called a homogenous transformation. We have recently showed how a desired homogenous mapping of the MAS in a n–D space can be prescribed by transient positions of n + 1 leaders placed at the vertices of a n–D polytope, called leading polytope [1–9]. In this article, we first minimize the acceleration norm with (i) initial and final positions of the leaders known and (ii) leaders (located at the vertices of the leading polytope) are constrained to move in such a way that the initial volume of the leading polytope is preserved during evolution. The followers learn the leader-determined homogenous map through local communication with each follower modeled as a double integrator. Proposed is a communication topology that requires every follower agent to update its position based on communication with n + 1 local agents. The weights of communication are uniquely specified by the initial positions of the agents. Simulation of a MAS moving in a plane validates the proposed communication topology.

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