Collision-free formation control of two-wheeled vehicles based on triangular LQ optimal regulator

This paper considers a formation control problem of two-wheeled vehicles. We first design a base controller based on the structured linear quadratic optimal regulator. The resulting optimal control gain is a lower triangular matrix; thus, agents communicate with each other in a top-down manner. However, vehicles may collide with each other under this control law since it is linear. To avoid collision of vehicles, we design a potential function by deforming the quadratic form of the stabilizing solution of the Riccati equation. The gradient of the potential function gives a control law that guarantees collision avoidance. The control law coincides with the optimal control law if vehicles are far from each other. The effectiveness of the proposed controller is confirmed by numerical simulation.