Formation control of differential-drive robots with input saturation and constraint on formation size

Cooperative control involves developing control strategies for individual robots that guarantee synchronized behavior of the states of all the robots in a team in some prescribed sense. In this work, we present a novel controller that achieves formation control for a group of differential-drive robots. First, we propose a nonlinear feedback control law that guarantees stable tracking of a reference trajectory for a single robot without exceeding the velocity limits of the robot. Using Lyapunov analysis, we obtain the necessary conditions on the control parameters and establish ultimate boundedness on error terms.  Next, we formulate the formation control problem as a trajectory tracking problem for the multi-robot system and solve it using the proposed controller. Additionally, we provide constraints on formation size for a planned reference trajectory, ensuring smooth cornering of multi-robot formation without exceeding actuation limits.