Ring-coupled unicycles: Boundedness, convergence, and control

In cyclic pursuit a platoon of vehicles are coupled in a unidirectional ring at the interaction level according to some control scheme. In the paper, a new cyclic pursuit control law is proposed, where each vehicle's linear speed and angular speed are proportional to the projection of its prey's position on its forward direction and lateral direction respectively. Through these interactions a cooperative behavior emerges and vehicles in the platoon eventually move at a constant speed on a circle with constant inter-vehicle spacings. The control scheme ensures ultimate boundedness and leads to only two stable equilibrium polygons. This contrasts with other cyclic pursuit control schemes, where vehicles may diverge to infinity and there are more stable equilibrium polygons as the total number of vehicles increases. For this control scheme, ultimate boundedness is proved using the pseudo-linearization technique. Possible equilibrium polygons are analyzed and stability and convergence properties are established through root locus analysis of a complex characteristic polynomial. Design rules are discussed, showing how the radius of the circle they converge to is controlled by an appropriate choice of control parameters.