Optimal internal force design for formation control of multi-agent systems

This paper proposes a method for designing a control law for a distributed cooperative formation control of multi-agent systems that positively utilizes self-equilibrium conditions on the basis of the force density method. The force density method is widely used in structural mechanics, and enables us to design the equilibrium of axially loaded structures (tensegrity structures) with a non-zero internal force. The control law is derived from a potential function of virtual 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. Considering the trade-off between the stiffness of target formation and the control effort, we choose a design objective to minimize the maximum eigenvalue of the tangent stiffness matrix under a constraint of stability. Numerical examples show that the proposed method suppresses the maximum eigenvalue of the tangent stiffness matrix, and decreases the control effort by introducing the non-zero internal force.