Formation Tracking with Orientation Convergence for Groups of Unicycles

This paper presents three trajectory tracking control strategies for unicycle-type robots based on a leader-followers scheme. The leader robot converges asymptotically to a smooth trajectory, while the follower robots form an undirected open-chain configuration at the same time. It is also shown that the orientation angles of all the robots converge to the same value. The control laws are based on a dynamic extension of the kinematic model of each robot. The output function to be controlled is the midpoint of the wheel axis of every robot. This choice leads to an ill-defined control law when the robot is at rest. To avoid such singularities, a complementary control law is enabled momentarily when the linear velocity of the unicycles is close to zero. Finally, numerical simulations and real-time experiments show the performance of the control strategies.