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This paper proposes a cooperative formation control of multi-agent systems by using self-equilibrium condition based on the force-density method. The force-density method is widely used in structural mechanics, which enables us to design the equilibrium of axially loaded structures (tensegrity structures) with non-zero control force. The control law is derived from a potential function of linear springs connecting the agents. Replacing the design variables in linear springs by force density (control force per unit length) and member constant (product of spring constant and rest length), the design problems can be described as convex optimization problems. As an application of the proposed strategy, a control design method for multi-agent systems with communication time-delays is provided. Permissible time-delay is maximized by minimizing the maximum eigen value of the tangent rigidity matrix. Numerical examples show that the permissible time-delay is increased by introducing the non-zero internal force.

Formation Control for Multi-agent Systems by Using Self-equilibrium Condition