Coordinated path following control of unicycles along given convex loops via curve extension design

This paper utilizes a dynamic model of unicycles to address the convergence of vehicle formations about closed convex curves. By extending a convex loop along the vector from the center of loop to the point on the loop, a novel method of curve extension is proposed to construct a family of level curves. A loop function is introduced to design path following control subsystem and then incorporated into the arc-length function to sketch formation control subsystem. The backstepping technique is used in the control design under a bidirectional communication graph. By graph theory and Invariance-like theorem it is proved that the designed cooperative control system is asymptotically stable if the graph is connected. The proposed method is effective for a skewed superellipse, which is a type of curve that includes circles, ellipses, and rounded parallelograms.