Scaling control of circular formation of agents with different reference variables

This paper addresses scaling control problem for multi-agent systems with nonlinear dynamics. The purpose is here to design the scaling control law in three cases distinguished by using different time-varying reference variables (angular velocity, linear velocity and radius) respectively to form a circular formation whose center is fixed, simultaneously with the requirement that all the desired distances between neighboring agents are equal. We show that three different control problems are possible in such cases: 1) a scaling motion with angular velocity is a constant, but linear velocity is a time-varying reference variable; 2) a scaling motion with linear velocity is a constant, but angular velocity is a time-varying reference variable; 3) a scaling motion tracks a time-varying radius directly. In addition, by comparing the three cases, we discuss the results, and find their advantages and disadvantages. Numerical examples illustrate all results.